When an initial amount of è dollars is invested at r% annual interest compounded n times per year, the value of the account (4) after 1 years s given by the equation t r A=P(1+²)*** n nt Write an equation that represents the value in an account that starts out with an initial investment of $5000 and pays 10% interest compound monthly. Then use that equation to fill the table and use the table to graph the equation. B M

When an initial amount of è dollars is invested at r% annual interest compounded n times per year, the value of the account (4) after 1 years s given by the equation t r A=P(1+²)*** n nt Write an equation that represents the value in an account that starts out with an initial investment of $5000 and pays 10% interest compound monthly. Then use that equation to fill the table and use the table to graph the equation. B M

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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*Using Matlab* The current amount A of a principal P invested in a savings account paying an annual interest rate r is given by A = P(1+r/n)^(nt) where n is the number of times per year the interest is compounded. For continuous compounding, A = Pe^(rt). Suppose $10,000 is initially invested at 2.5 percent (r = 0.025). a. Plot A versus t for 0 ≤ t ≤ 20 years for four cases: continuous compounding, annual compounding (n = 1), quarterly compounding (n = 4), and monthly compounding (n = 12). Show all four cases on the same subplot and label each curve. On a second subplot, plot the difference between the amount obtained from continuous compounding and the other three cases. b. Redo part a, but plot A versus t on log-log and semilog plots. Which plot gives a straight line?
The current amount A of a principal P invested in a savings account paying an annual interest rate r is given by A = P(1+r/n)^(rt) where n is the number of times per year the interest is compounded. For continuous compounding, A = Pe^(rt). Suppose $10,000 is initially invested at 2.5 percent (r = 0.025). a. Plot A versus t for 0 ≤ t ≤ 20 years for four cases: continuous compounding, annual compounding (n = 1), quarterly compounding (n = 4), and monthly compounding (n = 12). Show all four cases on the same subplot and label each curve. On a second subplot, plot the difference between the amount obtained from continuous compounding and the other three cases. b. Redo part a, but plot A versus t on log-log and semilog plots. Which plot gives a straight line?
To calculate how many years (n) an investment (P) must be kept in an account that earns interest at i%, in order to triple in amount, which of the following expressions should be used? (a) n = -P + F(P/F, i%, n) (b) n = [log (F/P)]/[log (1+ i%)] (c) n = [ In(– P +F)]/[In i%] (d) n = -F(1 + i%)P
set up an equation and solve each problem. Suppose that $500 is invested at a certain rate of interest compounded annually for 2 years. If the accumulated value at the end of 2 years is $594.05, find the rate of interest.
For each of the following situations involving annulties, solve for the unknown. Assume that interest is compounded annually and that all annulty amounts are received at the end of each period. (/= Interest rate, and n = number of years) Note: Use tables, Excel, or a financial calculator. Round your final answers to nearest whole dollar amount. (FV of $1, PV of $1, FVA of $1, PVA of $1, FVAD of $1 and PVAD of $1) 1. 2. 3. 4. 5. Present Value 248, 196 442,750 650,000 175,000 Annuity Amount $ 5,000 80,000 60,000 155,040 8% 11% 10% n = 5 4 10 4
If you deposit $P into a savings account that earns interest at a rate of i% per month for n years, the future worth in year n is represented by all of the following equations, except: (a) F = $P(F∕P, effective i/month, 12n) (b) F = $P(F∕P, effective i/quarter, 3n) (c) F = $P(F∕P, effective i/6-month, 2n) (d) F = $P(F∕P, effective i/year, n)
For the following exercise, use the compound interest formula, A(t) = P 1 + r n nt , where money is measured in dollars.After a certain number of years, the value of an investment account is represented by the expression 10,950 1 + 0.03 2 24 . How many years had the account been accumulating interest? yr
For each of the following situations involving single amounts, solve for the unknown. Assume that interest is compounded annually. (/= interest rate, and n=number of years) Note: Use tables, Excel, or a financial calculator. Round your final answers to nearest whole dollar amount. (FV of $1. PV of $1. EVA of $1. PVA of $1. FVAD of $1 and PVAD of $1) 1. 2 3. 4. 5. Present Value Future Value 1 $ 36,600 $ 62,000 $ 28,644 $ 76,000 $ 11,758 $ 45,500 68.822 $ 155,000 13,796 $ $ 5% 7% 8% n 20 12 10
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%
Suppose $100 is invested at the end of each year for the next 5 years into an account paying an interest rate r% p.a. How much can be drawn at the end of the 5 years? Approach (i) The first $100 is contributed in one year's time and has to wait 4 years to "mature". Write an equation describing this. (ii) The second $100 is contributed in two year's time and has to wait 3 years to "mature". Write an equation describing this. (iii) The third $100 is contributed in three year's time and has to wait 2 years to "mature". Write an equation describing this. (iv) Continue with this logic and sum all the matured values expressed
Calculate the future value of the following single amounts. (FV of $1, PV of $1, FVA of $1, and PVA of $1) (Use tables, Excel, or a financial calculator. Round your answers to 2 decimal places.) 1. 2 3. Initial Annual Investment Rate $ 7,200 5,200 8,200 8% 8% 8% Interest Compounded Annually Semiannually Quarterly Period Invested 9 years 6 years 3 years Future Value
For each of the following situations involving single amounts, solve for the unknown. Assume that interest is compounded annually. (i= interest rate, and n = number of years) Note: Use tables, Excel, or a financial calculator. Round your final answers to nearest whole dollar amount. (FV of $1, PV of $1, FVA of $1, PVA of $1, FVAD of $1 and PVAD of $1) 1. 2. 3. 4. 5. Present Value Future Value 80,000 94,000 50,000 200,000 $ $ $ $ $ 31,841 $ 15,762 $ 84,482 $ 13,291 i 7% 8% 9% n 9 16 10 15 1

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