Suppose you deposit m dollars at the beginning of every month in a savings account that earns a monthly interest rate of r. For an initial investment of m dollars, the amount of money in your account at the beginning of the second month is the sum of your second deposit and your initial deposit plus interest. Denote by An the amount of money in your account in the nth month. 1. Explain why A₁ = m dollars. 2. Explain why A₂ = m+m(1 + r) dollars. 3. Write down explicit expressions for A3 and A4. This is the crucial step. 4. Explain why An = m+m(1 + r) + m(1+r)²+...+m(1+r)n-¹ dollars. 5. Use the formula for a geometric sum to show that An = m (1+r)" - 1 T dollars. 6. If your account has a monthly interest rate r = 0.002 and you deposit $200 monthly for 5 years, how much money will you have in your account after the 5 years? (Hint: How many months?)

Suppose you deposit m dollars at the beginning of every month in a savings account that earns a monthly interest rate of r. For an initial investment of m dollars, the amount of money in your account at the beginning of the second month is the sum of your second deposit and your initial deposit plus interest. Denote by An the amount of money in your account in the nth month. 1. Explain why A₁ = m dollars. 2. Explain why A₂ = m+m(1 + r) dollars. 3. Write down explicit expressions for A3 and A4. This is the crucial step. 4. Explain why An = m+m(1 + r) + m(1+r)²+...+m(1+r)n-¹ dollars. 5. Use the formula for a geometric sum to show that An = m (1+r)" - 1 T dollars. 6. If your account has a monthly interest rate r = 0.002 and you deposit $200 monthly for 5 years, how much money will you have in your account after the 5 years? (Hint: How many months?)

Essentials Of Investments

11th Edition

ISBN:9781260013924

Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Chapter1: Investments: Background And Issues

Section: Chapter Questions

Problem 1PS

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Compute and compare the following interests situations if you deposit $2500 into an account with 3.5% interest for 10 years. 20) The account pays simple interest. 21) The account pays compounding interest monthly. 22) The account pasy continuously compounding interest. 23) How much difference is there between the three different types of interest? Explain.
For each of the following situations involving annuities, solve for the unknown. Assume that interest is compounded annually and that all annuity amounts are received at the end of each period. (i = interest rate, and n = number of years) (FV of $1, PV of $1, FVA of $1, PVA of $1, FVAD of $1 and PVAD of $1) (Use appropriate factor(s) from the tables provided. Round your final answers to nearest whole dollar amount.) Present Value Annuity Amount i = n = 1. ? $2,400 8% 5 2. 533,082 140,000 ? 4 3. 583,150 180,000 9% ? 4. 530,000 75,502 ? 8 5. 235,000 ? 10% 4
For each of the following situations involving annuities, solve for the unknown. Assume that interest is compounded annually and that all annuity amounts are received at the end of each period. (i=interest rate, and n=number of years)(FV of $1, PV of $1, FVA of $1, PVA of $1, FVAD of 1$ and PVAD of $1) (Use appropriate factor (s) from the tables provided. Round your final answers to nearest whole dollar amount.) Present Value Annuity Amount i= n= ______________ $ 2,600 8% 5 507,866 135,000 _____ 4 661,241 170,000 9% ____ 540,000 78,557 _____ 8 230,000 _____________ 10% 4
Suppose you deposit $1,181.00 into an account 5.00 years from today. Exactly 18.00 years from today the account is worth $1,800.00. What was the account's interest rate?
Task: Assume that at time 0 a sum L is lent for a series of n yearly payments. The rth payment, of amount x, is due at the end of the rth year. Let the effective annual interest rate for the rth year be i,. Give an identity which expresses L in terms of the x, and i,. Answer: The identity is [ Select ] [ Select ] L = x_1 (1+i_1)^(-1) + x_2 (1+i_1)^(-1) (1+i_2)^(-2) + .. + x_n (1+i_1)^(-1) (1+i_2)^(-2) ... (1+i_n)^(-n) L = x_1 (1+i_1) + x_2 (1+i_1) (1+i_2) + ... + x_n (1+i_1) (1+i_2) ... (1+i_n) L = x_1 (1+i_1)^(-1) + x_2 (1+i_1)^(-1) (1+i_2)^(-1) + .. + x_n (1+i_1)^(-1) (1+i_2)^(-1) ... (1+i_n)^(-1) Question 3 L = x_1 (1+i_1) + x_2 (1+i_1) (1+i_2)^2 + ... + x_n (1+i_1) (1+i_2)^2 ... (1+i_n)^n
A certain some of money P draws interest compounded continuously. If a certain time there are Po dollars in the account, determine the time when the financial attains the value of 2Po dollars if the annual interest rate at 2%
Write TRUE if the statement is true and FALSE if otherwise. 1. Compounding refers to the earning of interest on interest. 2. Discounting refers to the process of bringing the future back to the present. 3. The more frequently interest is compounded, the larger will be the final or terminal amount. 4. It takes longer than 8 years to retire a $24,000 loan at 8% if the annual payment is $3,000. 5. An annuity of $100 for 10 years is currently lessvaluable if interest rates are 10% instead of 12%. 6. If a person buys a stock for $10 and sells it after 10years for $20, the annual compound return is 10%. 7. Higher rates of interest are associated with greater present values. 8. If interest rates are 9 percent, an annuity of $100 for 10 years is to be preferred to $1,000 after 10 years. 9. If a bank pays 5 percent compounded semi-annually, the true rate of interest is less than 5 percent annually.
Solve the problem. solve using the formula for the future value of an ordinary annuity. given the monthly payment, capital, the annual interest rate, are, and the number of monthly payments, antique, find the future value of the annuity. R=$1300; r = 8.5%; nt= 17 A) $24,398.04 B) $17,548.36 C) $23,397.81 D) $24,198.38 Please search only correct answer as I am | paying for this and I keep receiving incorrect one
Assume that at the beginning of the year, you purchase an investment for $2,500 that pays $67 annual income. Also assume that the investment's value has decreased to $2,350 at the end of the year. a. What is the rate of return for this investment? b. Is the rate of return a positive or a negative number? Complete this question by entering your answers in the tabs below. Req 1 Req 2 What is the rate of return for this investment? Note: Enter your answer as a percent rounded to 2 decimal places. Input the amount as a positive value. Rate of return % Req 1 Req 2 >
Suppose you deposit $9,000 into your bank account at the beginning of each of the next 5 years (i.e., the first deposit is today). If the interest rate is 9%, how much would you have accumulated at the end of 5 years?Enter your response below (rounded to 2 decimal places).
K Suppose you receive $500 at the end of each year for the next three years. a. If the interest rate is 7%, what is the present value of these cash flows? b. What is the future value in three years of the present value you computed in (a)? c. Suppose you deposit the cash flows in a bank account that pays 7% interest per year. What is the balance in the account at the end of each of the next three years (after your deposit is made)? How does the final bank balance compare with your answer in (b)? a. The present value of the cash flow is $ (Round to the nearest cent)
For TVM calculator: Write each known variable’s value as it appears in the calculator and use a question mark for the missing variable. Then, in the space provided write the missing variable’s value, as it appears in the calculator. Finally, write your final answer in context, with units, as a complete sentence. Donald is looking to invest in an account earning an interest rate of 1.75% compounded weekly and make weekly payments. If he wants $21,000 in 10 years, what do his payments need to be? N=520 I= 1.75 PV=? PMT=? FV= 21,000 P/Y=52 C/Y=52 Missing Variable Value __________________ Context Sentence:

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