Question

1.You do not plan on working the majority of your life before retiring, as your parents are doing. Instead, you believe a 20 year working career is sufficient to accumulate a retirement account value of $2,000,000. If you start today, how much will you have to deposit each month to reach $2,000,000 at retirement?Assume you will average a 7.00 percent annual rate of return and deposits will be made at the end of the month. Report the final answer as dollars and cents.

2. You plan on working for the next 35 years before you retiring and you would like to accumulate $2,000,000 when you stop working. If you start today, how much will you have to deposit each month to reach $2,000,000 at retirement? assume you will average a 7.00 percent annual rate of return and deposits will be made at the end of the month. report answer as dollars and cents.

3. At what rate of interest must $100 be compounded annually for it to grow to $214.11 in 12 years?

Answer 1

Qs 1 & 2 are the same. So I'm answering at once.

Ans .1) Target amount = $2,000,000, Annual Rate of Return = 7%, Time = 20yrs , Deposits to be made at the end of the month.

Monthly Rate of Return = 7/12 = 0.583%

Total Number of months = 12*20 = 240

Let monthly deposits be P

As deposits are made at the end of the month, the deposits won't be compounded at the end of month.

The expression for Annual compounding factor is

As here the compounding is done monthly so n=240, r= 0.583%

P*(520.67)=2,000,000

Ans. 2)

The expression for compounding is

Here, n=12 yrs , P= $100 , Compounded Value = $214.11

As,  

r = 6.55%