Math help!! Finance

Question

Suppose you want to have $300,000 for retirement in 30 years. Your account earns 9% interest.

a) How much would you need to deposit in the account each month?

b) How much interest will you earn?

c)  Suppose you waited 10 years to invest in the same retirement fund and have the same $300,000 for retirement at the same 9% interest. What amount will you have to deposit each month to match the value of your annuity?

Answer 1

a) $300,000 is a future value of your investment. FV=$300,000

Now you have $0, so the present value of your investment is $0.

9% is the annual interest rate, to make it monthly you should divide by 12. 9/12=0.75% per month

30 is number of annual periods. To calcalate number of months, you need to multiply it by 12. 30*12=360

You can solve this problem in excel (=pmt) or by using a financial calculator.

Set FV=$300,000

PV=$0

i=rate=0.75%

nper=360

PMT=? solve---> $163.87 monthly payment you need to make to reach $300,000 in 30 years

b) You earn 0.75% interest per month or 9% per annum

c) Now you have only 20 years left to invest which is 20*12=240 months. All other components are the same.

FV=$300,000

i=rate=0.75%

nper=240

PV=$0

PMT=? ----> $449.18 monthly payment you need to make to reach $300,000 in 20 years