1. Assume you have the following situations. Using the time value of money (TVM)
ID: 2640433 • Letter: 1
Question
1. Assume you have the following situations. Using the time value of money (TVM) concepts (formulas or tables) calculate the correct amount in each situation.
a. You have $10,000 to invest, at 5% annually and you will keep the money invested for 10 years. What will this amount grow to?
b. You will need $15,000 in 7 years when you want to take a world cruise. If you can earn 6% annually how much do you need to invest now, in order to have the amount needed for the cruise?
c. You are working on saving for retirement. You will reach full retirement age in 20 years, and you can invest $5000 each year and can earn 7% annually during this period. How much money will you have as you enter the retirement phase of your life, from this investment?
d. What is the amount a person would have to deposit today to be able to take out $5000 a year for 10 years from an account earning 8 percent annually?
Explanation / Answer
1)Amount=principal(1+Interest p.a )^no.of yrs
=10000(1+.05)^10= $16289
2) Substituting in above ,to calculate present value
15000=PV(1+0.06)^7
PV=15000 /1.06^7
=$9976
3) Initial amt =5000 ;i=7% or .07 ;n=20yrs.
Final amt =5000(1+0.07)^20
= $19348
4)This is calculating PV of annuity of 5000 for 10 yrs @8% p.a --using the formula
PV of an annuity=P (1-(1+r)^-n) /r
where P =Periodic payment ie 5000
r=rate of interest ie.8% or 0.08
n=no.of yrs ie.10
PV=5000(1-(1+.08)^-10) /0.08
= $33550
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