Question

Business Finance
Time Value of Money
Assignment 2
Solve following problems
Problem 1
Muffin Megabucks is considering two different savings plans. The first plan would have her deposit $500 every six months, and she would receive interest at a 7 percent annual rate, compounded semiannually. Under the second plan she would deposit $1,000 every year with a rate of interest of 7.5 percent, compounded annually. The initial deposit with Plan 1 would be made six months from now and, with Plan 2, one year hence.
a. What is the future (terminal) value of the first plan at the end of 10 years?
b. What is the future (terminal) value of the second plan at the end of 10 years?
c. Which plan should Muffin use, assuming that her only concern is with the value of her savings at the end of 10 years?
d. Would your answer change if the rate of interest on the second plan were 7 percent?

Problem 2
Selyn Cohen is 63 years old and recently retired. He wishes to provide retirement income for himself and is considering an annuity contract with the Philo Life Insurance Company. Such a contract pays him an equal-dollar amount each year that he lives. For this cash-flow stream, he must put up a specific amount of money at the beginning. According to actuary tables, his life expectancy is 15 years, and that is the duration on which the insurance company bases its calculations regardless of how long he actually lives.
a. If Philo Life uses a compound annual interest rate of 5 percent in its calculations, what must Cohen pay at the outset for an annuity to provide him with $10,000 per year? (Assume that the expected annual payments are at the end of each of the 15 years.)
b. What would be the purchase price if the compound annual interest rate is 10 percent?
c. Cohen had $30,000 to put into an annuity. How much would he receive each year if the insurance company uses a 5 percent compound annual interest rate in its calculations?

Problem 3
A Dillonvale, Ohio, man saved pennies for 65 years. When he finally decided to cash them in, he had roughly 8 million of them (or $80,000 worth), filling 40 trash cans. On average, the man saved $1,230 worth of pennies a year. If he had deposited the pennies saved each year, at each year’s end, into a savings account earning 5 percent compound annual interest, how much would he have had in this account after 65 years of saving? How much more “cents” (sense) would this have meant for our “penny saver” compared with simply putting his pennies into trash cans?
Problem 4
Assume that you will be opening a savings account today by depositing $100,000. The savings account pays 5 percent compound annual interest, and this rate is assumed to remain in effect for all future periods. Four years from today you will withdraw R dollars. You will continue to make additional annual withdrawals of R dollars for a while longer – making your last withdrawal at the end of year 9 – to achieve the following pattern of cash flows over time. (Note: Today is time period zero; one year from today is the end of time period 1; etc.)

How large must R be to leave you with exactly a zero balance after your final R withdrawal is made at the end of year 9?

Answer 1

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Answer 2

Top answer · 9 votes

a. Plan 1 Amount: $500, rate:7%/2=0.035, number of period (n)=20-1=19 FVA=Amount* ( (1+rate)^n)-1)/rate =500*(((1.035)^19)-1)/0.035=13178.59 Amount:

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