The rate of return of a bond Introduction: Rate of return refers to the gain or loss on the investment. It also refers to the increase or decrease in the capital value of an investment. The future value of money refers to the amount of dollars that an investment grows over a definite period at a particular rate of interest rate. In other words, it refers to the future value of present cash investments.

Question

Want to see more full solutions like this?

Answer 1

Question

Chapter 5, Problem 16QP

a)

Summary Introduction

To calculate: The rate of return of a bond

Introduction:

Rate of return refers to the gain or loss on the investment. It also refers to the increase or decrease in the capital value of an investment.

The future value of money refers to the amount of dollars that an investment grows over a definite period at a particular rate of interest rate. In other words, it refers to the future value of present cash investments.

a)

Expert Solution

Answer to Problem 16QP

A bond with a face value of $50 would double its value in 20 years if the rate of return is 3.53%.

Explanation of Solution

Given information:

Person X purchased a bond worth $50. He plans to hold it for 20 years until the value of the bond doubles.

The formula to calculate the rate of return:

P×(1+r)t=FV

Where,

“P” refers to the principal amount invested

“r” refers to the simple rate of interest

“t” refers to the number of years or periods of investment

“FV” refers to the future value or the current market value

Compute the rate of return:

The present value of the bond is $50. He plans to invest for 20 years until the value of the bond doubles. Hence, the future value of the bond will be $100 ($50×2) .

P×(1+r)t=FV$50×(1+r)20=$100(1+r)20=$100$50(1+r)20=2

1+r=2120r=1.0353−1r=0.0353 or 3.53%

Hence, the rate of return is 3.53% per year.

b)

Summary Introduction

To calculate: The future value of the bond

Introduction:

Rate of return refers to the gain or loss on the investment. It also refers to the increase or decrease in the capital value of an investment.

The future value of money refers to the amount of dollars that an investment grows over a definite period at a particular rate of interest rate. In other words, it refers to the future value of present cash investments.

b)

Expert Solution

Answer to Problem 16QP

The value of the bond in 2024 will be $50.5.

Explanation of Solution

Given information:

Person X will purchase a bond worth $50 in 2014. He plans to hold it until 2024 or for 10 years. The rate of interest on the bond is 0.10 percent per year.

The formula to calculate the future value:

FV=PV×(1+r)t

Where,

“FV” refers to the future value or the current market value

“PV” refers to the present value

“r” refers to the simple rate of interest

“t” refers to the number of years or periods of investment

Compute the future value:

FV=PV×(1+r)t=$50×(1+0.001)10=$50×1.0100=$50.5

Hence, the future value of investment after 10 years is $50.5.

c)

Summary Introduction

To calculate: The rate of return

Introduction:

Rate of return refers to the gain or loss on the investment. It also refers to the increase or decrease in the capital value of an investment.

The future value of money refers to the amount of dollars that an investment grows over a definite period at a particular rate of interest rate. In other words, it refers to the future value of present cash investments.

c)

Expert Solution

Answer to Problem 16QP

The bond has to fetch a return of 7.18% per year to double its value in 2034.

Explanation of Solution

Given information:

Person X purchased a bond worth $50 in 2014. He plans to hold it until 2024 or for 10 years. The rate of interest on the bond is 0.10 percent per year. The future value of this bond in 2024 will be $50.50 (Refer to Part (b) of the solution). Instead of cashing the bond at $50.50, he plans to reinvest the bond value until the value of the bond doubles in 2034.

The formula to calculate the rate of return:

P×(1+r)t=FV

Where,

“P” refers to the principal amount invested

“r” refers to the simple rate of interest

“t” refers to the number of years or periods of investment

“FV” refers to the future value or the current market value

Compute the rate of return:

The present value of the bond is $50.50 in 2024. He plans to invest for 10 years until the value of the bond doubles in 2034. Hence, the future value of the bond will be $101 ($50.50×2) .

P×(1+r)t=FV$50.50×(1+r)10=$101(1+r)10=$101$50.50(1+r)10=2

1+r=2110r=1.0718−1r=0.0718 or 7.18%

Hence, the bond has to fetch a return of 7.18% per year to double its value in 2034.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Students have asked these similar questions

3. Present Value of Annuity and Perpetuity - Show your steps! (You must simplify your answer use the formula for Geometric series.) 1 A bond with a face value of y pays out interest at rate r annually. The discount rate you should use for the bond is i. (That is, the present value of $1 received a year from now is $11, and the present value of 1 dollar received 2 years from now is $- .) What is the present value of owning the bond that pays its first interest a year from now if (a) The bond pays interest for n years and pays back the face value at the last year. (b) The bond pays interest forever and never pays back the face value. (1+i)²

You are deciding whether to buy a bond. The bond will pay out $1,000 in 5 years. But there is uncertainty over the interest rate. Between now and year 1 (period 0 and period 1), uncertainty will be resolved immediately after time 0. There is • 50 percent chance r = 0.1 • 50 percent chance r = 0.05 Interest compounds annually. What is the expected value of the bond?.

4. Suppose that an investment institution offers you two kinds of bonds and you are willing to take one of them. The first bond, called 'Bond A1' pays you $5000 in 10 years, while the second bond, called 'Bond B1' pays you the same amount but in 20 years. а. If the interest rate is 5%, what is the value of each bond today? Which bond is worth more? Why? b. If the interest rate increases to 8%, what is the value of each bond? Which bond has a larger percentage change in value? After knowing the answer of A and B, you will С. be able to complete this sentence: "The value of bond [rises / falls] when the interest rate increases, and bonds with longer time to maturity are [more/less] sensitive to changes in the interest rate"

Answer 2

Question

Chapter 5, Problem 16QP

a)

Summary Introduction

To calculate: The rate of return of a bond

Introduction:

Rate of return refers to the gain or loss on the investment. It also refers to the increase or decrease in the capital value of an investment.

The future value of money refers to the amount of dollars that an investment grows over a definite period at a particular rate of interest rate. In other words, it refers to the future value of present cash investments.

a)

Expert Solution

Answer to Problem 16QP

A bond with a face value of $50 would double its value in 20 years if the rate of return is 3.53%.

Explanation of Solution

Given information:

Person X purchased a bond worth $50. He plans to hold it for 20 years until the value of the bond doubles.

The formula to calculate the rate of return:

P×(1+r)t=FV

Where,

“P” refers to the principal amount invested

“r” refers to the simple rate of interest

“t” refers to the number of years or periods of investment

“FV” refers to the future value or the current market value

Compute the rate of return:

The present value of the bond is $50. He plans to invest for 20 years until the value of the bond doubles. Hence, the future value of the bond will be $100 ($50×2) .

P×(1+r)t=FV$50×(1+r)20=$100(1+r)20=$100$50(1+r)20=2

1+r=2120r=1.0353−1r=0.0353 or 3.53%

Hence, the rate of return is 3.53% per year.

b)

Summary Introduction

To calculate: The future value of the bond

Introduction:

Rate of return refers to the gain or loss on the investment. It also refers to the increase or decrease in the capital value of an investment.

The future value of money refers to the amount of dollars that an investment grows over a definite period at a particular rate of interest rate. In other words, it refers to the future value of present cash investments.

b)

Expert Solution

Answer to Problem 16QP

The value of the bond in 2024 will be $50.5.

Explanation of Solution

Given information:

Person X will purchase a bond worth $50 in 2014. He plans to hold it until 2024 or for 10 years. The rate of interest on the bond is 0.10 percent per year.

The formula to calculate the future value:

FV=PV×(1+r)t

Where,

“FV” refers to the future value or the current market value

“PV” refers to the present value

“r” refers to the simple rate of interest

“t” refers to the number of years or periods of investment

Compute the future value:

FV=PV×(1+r)t=$50×(1+0.001)10=$50×1.0100=$50.5

Hence, the future value of investment after 10 years is $50.5.

c)

Summary Introduction

To calculate: The rate of return

Introduction:

Rate of return refers to the gain or loss on the investment. It also refers to the increase or decrease in the capital value of an investment.

The future value of money refers to the amount of dollars that an investment grows over a definite period at a particular rate of interest rate. In other words, it refers to the future value of present cash investments.

c)

Expert Solution

Answer to Problem 16QP

The bond has to fetch a return of 7.18% per year to double its value in 2034.

Explanation of Solution

Given information:

Person X purchased a bond worth $50 in 2014. He plans to hold it until 2024 or for 10 years. The rate of interest on the bond is 0.10 percent per year. The future value of this bond in 2024 will be $50.50 (Refer to Part (b) of the solution). Instead of cashing the bond at $50.50, he plans to reinvest the bond value until the value of the bond doubles in 2034.

The formula to calculate the rate of return:

P×(1+r)t=FV

Where,

“P” refers to the principal amount invested

“r” refers to the simple rate of interest

“t” refers to the number of years or periods of investment

“FV” refers to the future value or the current market value

Compute the rate of return:

The present value of the bond is $50.50 in 2024. He plans to invest for 10 years until the value of the bond doubles in 2034. Hence, the future value of the bond will be $101 ($50.50×2) .

P×(1+r)t=FV$50.50×(1+r)10=$101(1+r)10=$101$50.50(1+r)10=2

1+r=2110r=1.0718−1r=0.0718 or 7.18%

Hence, the bond has to fetch a return of 7.18% per year to double its value in 2034.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 3

Question

Chapter 5, Problem 16QP

a)

Summary Introduction

To calculate: The rate of return of a bond

Introduction:

Rate of return refers to the gain or loss on the investment. It also refers to the increase or decrease in the capital value of an investment.

The future value of money refers to the amount of dollars that an investment grows over a definite period at a particular rate of interest rate. In other words, it refers to the future value of present cash investments.

a)

Expert Solution

Answer to Problem 16QP

A bond with a face value of $50 would double its value in 20 years if the rate of return is 3.53%.

Explanation of Solution

Given information:

Person X purchased a bond worth $50. He plans to hold it for 20 years until the value of the bond doubles.

The formula to calculate the rate of return:

P×(1+r)t=FV

Where,

“P” refers to the principal amount invested

“r” refers to the simple rate of interest

“t” refers to the number of years or periods of investment

“FV” refers to the future value or the current market value

Compute the rate of return:

The present value of the bond is $50. He plans to invest for 20 years until the value of the bond doubles. Hence, the future value of the bond will be $100 ($50×2) .

P×(1+r)t=FV$50×(1+r)20=$100(1+r)20=$100$50(1+r)20=2

1+r=2120r=1.0353−1r=0.0353 or 3.53%

Hence, the rate of return is 3.53% per year.

b)

Summary Introduction

To calculate: The future value of the bond

Introduction:

Rate of return refers to the gain or loss on the investment. It also refers to the increase or decrease in the capital value of an investment.

The future value of money refers to the amount of dollars that an investment grows over a definite period at a particular rate of interest rate. In other words, it refers to the future value of present cash investments.

b)

Expert Solution

Answer to Problem 16QP

The value of the bond in 2024 will be $50.5.

Explanation of Solution

Given information:

Person X will purchase a bond worth $50 in 2014. He plans to hold it until 2024 or for 10 years. The rate of interest on the bond is 0.10 percent per year.

The formula to calculate the future value:

FV=PV×(1+r)t

Where,

“FV” refers to the future value or the current market value

“PV” refers to the present value

“r” refers to the simple rate of interest

“t” refers to the number of years or periods of investment

Compute the future value:

FV=PV×(1+r)t=$50×(1+0.001)10=$50×1.0100=$50.5

Hence, the future value of investment after 10 years is $50.5.

c)

Summary Introduction

To calculate: The rate of return

Introduction:

Rate of return refers to the gain or loss on the investment. It also refers to the increase or decrease in the capital value of an investment.

The future value of money refers to the amount of dollars that an investment grows over a definite period at a particular rate of interest rate. In other words, it refers to the future value of present cash investments.

c)

Expert Solution

Answer to Problem 16QP

The bond has to fetch a return of 7.18% per year to double its value in 2034.

Explanation of Solution

Given information:

Person X purchased a bond worth $50 in 2014. He plans to hold it until 2024 or for 10 years. The rate of interest on the bond is 0.10 percent per year. The future value of this bond in 2024 will be $50.50 (Refer to Part (b) of the solution). Instead of cashing the bond at $50.50, he plans to reinvest the bond value until the value of the bond doubles in 2034.

The formula to calculate the rate of return:

P×(1+r)t=FV

Where,

“P” refers to the principal amount invested

“r” refers to the simple rate of interest

“t” refers to the number of years or periods of investment

“FV” refers to the future value or the current market value

Compute the rate of return:

The present value of the bond is $50.50 in 2024. He plans to invest for 10 years until the value of the bond doubles in 2034. Hence, the future value of the bond will be $101 ($50.50×2) .

P×(1+r)t=FV$50.50×(1+r)10=$101(1+r)10=$101$50.50(1+r)10=2

1+r=2110r=1.0718−1r=0.0718 or 7.18%

Hence, the bond has to fetch a return of 7.18% per year to double its value in 2034.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 4

Question

Chapter 5, Problem 16QP

a)

Summary Introduction

To calculate: The rate of return of a bond

Introduction:

Rate of return refers to the gain or loss on the investment. It also refers to the increase or decrease in the capital value of an investment.

The future value of money refers to the amount of dollars that an investment grows over a definite period at a particular rate of interest rate. In other words, it refers to the future value of present cash investments.

a)

Expert Solution

Answer to Problem 16QP

A bond with a face value of $50 would double its value in 20 years if the rate of return is 3.53%.

Explanation of Solution

Given information:

Person X purchased a bond worth $50. He plans to hold it for 20 years until the value of the bond doubles.

The formula to calculate the rate of return:

P×(1+r)t=FV

Where,

“P” refers to the principal amount invested

“r” refers to the simple rate of interest

“t” refers to the number of years or periods of investment

“FV” refers to the future value or the current market value

Compute the rate of return:

The present value of the bond is $50. He plans to invest for 20 years until the value of the bond doubles. Hence, the future value of the bond will be $100 ($50×2) .

P×(1+r)t=FV$50×(1+r)20=$100(1+r)20=$100$50(1+r)20=2

1+r=2120r=1.0353−1r=0.0353 or 3.53%

Hence, the rate of return is 3.53% per year.

b)

Summary Introduction

To calculate: The future value of the bond

Introduction:

Rate of return refers to the gain or loss on the investment. It also refers to the increase or decrease in the capital value of an investment.

The future value of money refers to the amount of dollars that an investment grows over a definite period at a particular rate of interest rate. In other words, it refers to the future value of present cash investments.

b)

Expert Solution

Answer to Problem 16QP

The value of the bond in 2024 will be $50.5.

Explanation of Solution

Given information:

Person X will purchase a bond worth $50 in 2014. He plans to hold it until 2024 or for 10 years. The rate of interest on the bond is 0.10 percent per year.

The formula to calculate the future value:

FV=PV×(1+r)t

Where,

“FV” refers to the future value or the current market value

“PV” refers to the present value

“r” refers to the simple rate of interest

“t” refers to the number of years or periods of investment

Compute the future value:

FV=PV×(1+r)t=$50×(1+0.001)10=$50×1.0100=$50.5

Hence, the future value of investment after 10 years is $50.5.

c)

Summary Introduction

To calculate: The rate of return

Introduction:

Rate of return refers to the gain or loss on the investment. It also refers to the increase or decrease in the capital value of an investment.

The future value of money refers to the amount of dollars that an investment grows over a definite period at a particular rate of interest rate. In other words, it refers to the future value of present cash investments.

c)

Expert Solution

Answer to Problem 16QP

The bond has to fetch a return of 7.18% per year to double its value in 2034.

Explanation of Solution

Given information:

Person X purchased a bond worth $50 in 2014. He plans to hold it until 2024 or for 10 years. The rate of interest on the bond is 0.10 percent per year. The future value of this bond in 2024 will be $50.50 (Refer to Part (b) of the solution). Instead of cashing the bond at $50.50, he plans to reinvest the bond value until the value of the bond doubles in 2034.

The formula to calculate the rate of return:

P×(1+r)t=FV

Where,

“P” refers to the principal amount invested

“r” refers to the simple rate of interest

“t” refers to the number of years or periods of investment

“FV” refers to the future value or the current market value

Compute the rate of return:

The present value of the bond is $50.50 in 2024. He plans to invest for 10 years until the value of the bond doubles in 2034. Hence, the future value of the bond will be $101 ($50.50×2) .

P×(1+r)t=FV$50.50×(1+r)10=$101(1+r)10=$101$50.50(1+r)10=2

1+r=2110r=1.0718−1r=0.0718 or 7.18%

Hence, the bond has to fetch a return of 7.18% per year to double its value in 2034.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 5

Chapter 5, Problem 16QP

a)

Summary Introduction

To calculate: The rate of return of a bond

Introduction:

Rate of return refers to the gain or loss on the investment. It also refers to the increase or decrease in the capital value of an investment.

The future value of money refers to the amount of dollars that an investment grows over a definite period at a particular rate of interest rate. In other words, it refers to the future value of present cash investments.

a)

Expert Solution

Answer to Problem 16QP

A bond with a face value of $50 would double its value in 20 years if the rate of return is 3.53%.

Explanation of Solution

Given information:

Person X purchased a bond worth $50. He plans to hold it for 20 years until the value of the bond doubles.

The formula to calculate the rate of return:

P×(1+r)t=FV

Where,

“P” refers to the principal amount invested

“r” refers to the simple rate of interest

“t” refers to the number of years or periods of investment

“FV” refers to the future value or the current market value

Compute the rate of return:

The present value of the bond is $50. He plans to invest for 20 years until the value of the bond doubles. Hence, the future value of the bond will be $100 ($50×2) .

P×(1+r)t=FV$50×(1+r)20=$100(1+r)20=$100$50(1+r)20=2

1+r=2120r=1.0353−1r=0.0353 or 3.53%

Hence, the rate of return is 3.53% per year.

b)

Summary Introduction

To calculate: The future value of the bond

Introduction:

Rate of return refers to the gain or loss on the investment. It also refers to the increase or decrease in the capital value of an investment.

The future value of money refers to the amount of dollars that an investment grows over a definite period at a particular rate of interest rate. In other words, it refers to the future value of present cash investments.

b)

Expert Solution

Answer to Problem 16QP

The value of the bond in 2024 will be $50.5.

Explanation of Solution

Given information:

Person X will purchase a bond worth $50 in 2014. He plans to hold it until 2024 or for 10 years. The rate of interest on the bond is 0.10 percent per year.

The formula to calculate the future value:

FV=PV×(1+r)t

Where,

“FV” refers to the future value or the current market value

“PV” refers to the present value

“r” refers to the simple rate of interest

“t” refers to the number of years or periods of investment

Compute the future value:

FV=PV×(1+r)t=$50×(1+0.001)10=$50×1.0100=$50.5

Hence, the future value of investment after 10 years is $50.5.

c)

Summary Introduction

To calculate: The rate of return

Introduction:

Rate of return refers to the gain or loss on the investment. It also refers to the increase or decrease in the capital value of an investment.

The future value of money refers to the amount of dollars that an investment grows over a definite period at a particular rate of interest rate. In other words, it refers to the future value of present cash investments.

c)

Expert Solution

Answer to Problem 16QP

The bond has to fetch a return of 7.18% per year to double its value in 2034.

Explanation of Solution

Given information:

Person X purchased a bond worth $50 in 2014. He plans to hold it until 2024 or for 10 years. The rate of interest on the bond is 0.10 percent per year. The future value of this bond in 2024 will be $50.50 (Refer to Part (b) of the solution). Instead of cashing the bond at $50.50, he plans to reinvest the bond value until the value of the bond doubles in 2034.

The formula to calculate the rate of return:

P×(1+r)t=FV

Where,

“P” refers to the principal amount invested

“r” refers to the simple rate of interest

“t” refers to the number of years or periods of investment

“FV” refers to the future value or the current market value

Compute the rate of return:

The present value of the bond is $50.50 in 2024. He plans to invest for 10 years until the value of the bond doubles in 2034. Hence, the future value of the bond will be $101 ($50.50×2) .

P×(1+r)t=FV$50.50×(1+r)10=$101(1+r)10=$101$50.50(1+r)10=2

1+r=2110r=1.0718−1r=0.0718 or 7.18%

Hence, the bond has to fetch a return of 7.18% per year to double its value in 2034.

Answer 6

Chapter 5, Problem 16QP

a)

Summary Introduction

To calculate: The rate of return of a bond

Introduction:

Rate of return refers to the gain or loss on the investment. It also refers to the increase or decrease in the capital value of an investment.

The future value of money refers to the amount of dollars that an investment grows over a definite period at a particular rate of interest rate. In other words, it refers to the future value of present cash investments.

a)

Expert Solution

Answer to Problem 16QP

A bond with a face value of $50 would double its value in 20 years if the rate of return is 3.53%.

Explanation of Solution

Given information:

Person X purchased a bond worth $50. He plans to hold it for 20 years until the value of the bond doubles.

The formula to calculate the rate of return:

P×(1+r)t=FV

Where,

“P” refers to the principal amount invested

“r” refers to the simple rate of interest

“t” refers to the number of years or periods of investment

“FV” refers to the future value or the current market value

Compute the rate of return:

The present value of the bond is $50. He plans to invest for 20 years until the value of the bond doubles. Hence, the future value of the bond will be $100 ($50×2) .

P×(1+r)t=FV$50×(1+r)20=$100(1+r)20=$100$50(1+r)20=2

1+r=2120r=1.0353−1r=0.0353 or 3.53%

Hence, the rate of return is 3.53% per year.

Answer 7

Chapter 5, Problem 16QP

a)

Summary Introduction

To calculate: The rate of return of a bond

Introduction:

Rate of return refers to the gain or loss on the investment. It also refers to the increase or decrease in the capital value of an investment.

The future value of money refers to the amount of dollars that an investment grows over a definite period at a particular rate of interest rate. In other words, it refers to the future value of present cash investments.

Answer 8

a)

Expert Solution

Answer to Problem 16QP

A bond with a face value of $50 would double its value in 20 years if the rate of return is 3.53%.

Answer 9

a)

Expert Solution

Answer 10

a)

Expert Solution

Answer 11

Expert Solution

Answer 12

Explanation of Solution

Given information:

Person X purchased a bond worth $50. He plans to hold it for 20 years until the value of the bond doubles.

The formula to calculate the rate of return:

P×(1+r)t=FV

Where,

“P” refers to the principal amount invested

“r” refers to the simple rate of interest

“t” refers to the number of years or periods of investment

“FV” refers to the future value or the current market value

Compute the rate of return:

The present value of the bond is $50. He plans to invest for 20 years until the value of the bond doubles. Hence, the future value of the bond will be $100 ($50×2) .

P×(1+r)t=FV$50×(1+r)20=$100(1+r)20=$100$50(1+r)20=2

1+r=2120r=1.0353−1r=0.0353 or 3.53%

Hence, the rate of return is 3.53% per year.

Answer 13

b)

Summary Introduction

To calculate: The future value of the bond

Introduction:

Rate of return refers to the gain or loss on the investment. It also refers to the increase or decrease in the capital value of an investment.

The future value of money refers to the amount of dollars that an investment grows over a definite period at a particular rate of interest rate. In other words, it refers to the future value of present cash investments.

b)

Expert Solution

Answer to Problem 16QP

The value of the bond in 2024 will be $50.5.

Explanation of Solution

Given information:

Person X will purchase a bond worth $50 in 2014. He plans to hold it until 2024 or for 10 years. The rate of interest on the bond is 0.10 percent per year.

The formula to calculate the future value:

FV=PV×(1+r)t

Where,

“FV” refers to the future value or the current market value

“PV” refers to the present value

“r” refers to the simple rate of interest

“t” refers to the number of years or periods of investment

Compute the future value:

FV=PV×(1+r)t=$50×(1+0.001)10=$50×1.0100=$50.5

Hence, the future value of investment after 10 years is $50.5.

Answer 14

b)

Summary Introduction

To calculate: The future value of the bond

Introduction:

Rate of return refers to the gain or loss on the investment. It also refers to the increase or decrease in the capital value of an investment.

The future value of money refers to the amount of dollars that an investment grows over a definite period at a particular rate of interest rate. In other words, it refers to the future value of present cash investments.

Answer 15

b)

Expert Solution

Answer to Problem 16QP

The value of the bond in 2024 will be $50.5.

Answer 16

b)

Expert Solution

Answer 17

b)

Expert Solution

Answer 18

Expert Solution

Answer 19

Explanation of Solution

Given information:

Person X will purchase a bond worth $50 in 2014. He plans to hold it until 2024 or for 10 years. The rate of interest on the bond is 0.10 percent per year.

The formula to calculate the future value:

FV=PV×(1+r)t

Where,

“FV” refers to the future value or the current market value

“PV” refers to the present value

“r” refers to the simple rate of interest

“t” refers to the number of years or periods of investment

Compute the future value:

FV=PV×(1+r)t=$50×(1+0.001)10=$50×1.0100=$50.5

Hence, the future value of investment after 10 years is $50.5.

Answer 20

c)

Summary Introduction

To calculate: The rate of return

Introduction:

Rate of return refers to the gain or loss on the investment. It also refers to the increase or decrease in the capital value of an investment.

The future value of money refers to the amount of dollars that an investment grows over a definite period at a particular rate of interest rate. In other words, it refers to the future value of present cash investments.

c)

Expert Solution

Answer to Problem 16QP

The bond has to fetch a return of 7.18% per year to double its value in 2034.

Explanation of Solution

Given information:

Person X purchased a bond worth $50 in 2014. He plans to hold it until 2024 or for 10 years. The rate of interest on the bond is 0.10 percent per year. The future value of this bond in 2024 will be $50.50 (Refer to Part (b) of the solution). Instead of cashing the bond at $50.50, he plans to reinvest the bond value until the value of the bond doubles in 2034.

The formula to calculate the rate of return:

P×(1+r)t=FV

Where,

“P” refers to the principal amount invested

“r” refers to the simple rate of interest

“t” refers to the number of years or periods of investment

“FV” refers to the future value or the current market value

Compute the rate of return:

The present value of the bond is $50.50 in 2024. He plans to invest for 10 years until the value of the bond doubles in 2034. Hence, the future value of the bond will be $101 ($50.50×2) .

P×(1+r)t=FV$50.50×(1+r)10=$101(1+r)10=$101$50.50(1+r)10=2

1+r=2110r=1.0718−1r=0.0718 or 7.18%

Hence, the bond has to fetch a return of 7.18% per year to double its value in 2034.

Answer 21

c)

Summary Introduction

To calculate: The rate of return

Introduction:

Rate of return refers to the gain or loss on the investment. It also refers to the increase or decrease in the capital value of an investment.

The future value of money refers to the amount of dollars that an investment grows over a definite period at a particular rate of interest rate. In other words, it refers to the future value of present cash investments.

Answer 22

c)

Expert Solution

Answer to Problem 16QP

The bond has to fetch a return of 7.18% per year to double its value in 2034.

Answer 23

c)

Expert Solution

Answer 24

c)

Expert Solution

Answer 25

Expert Solution

Answer 26

Explanation of Solution

Given information:

Person X purchased a bond worth $50 in 2014. He plans to hold it until 2024 or for 10 years. The rate of interest on the bond is 0.10 percent per year. The future value of this bond in 2024 will be $50.50 (Refer to Part (b) of the solution). Instead of cashing the bond at $50.50, he plans to reinvest the bond value until the value of the bond doubles in 2034.

The formula to calculate the rate of return:

P×(1+r)t=FV

Where,

“P” refers to the principal amount invested

“r” refers to the simple rate of interest

“t” refers to the number of years or periods of investment

“FV” refers to the future value or the current market value

Compute the rate of return:

The present value of the bond is $50.50 in 2024. He plans to invest for 10 years until the value of the bond doubles in 2034. Hence, the future value of the bond will be $101 ($50.50×2) .

P×(1+r)t=FV$50.50×(1+r)10=$101(1+r)10=$101$50.50(1+r)10=2