Question

Mike is currently 35 years old and plans on retiring at the age of 65. Ideally, Mike would like to retire with $1,000,000.00.

A.How much would Mike have to deposit on a monthly basis to reach his goal if he can get a return of 10% compounded monthly?

B. If Mike can only deposit $350 on a monthly basis, what annual rate would he have to receive to reach his goal?

C.If Mike was quoted an APR of 11%, what is his effective annual rate with daily compounding?

if you can show steps on financial calculator that would be really helpful! thanks!

Answer 1

Information provided:

Future value= $1,000,000

Time= 65 years – 35 years= 30 years*12= 360 months

Interest rate= 10%/12= 0.8333% per month

a.The amount of monthly deposit is calculated by entering the below in a financial calculator:

FV= 1,000,000

N= 360

I/Y= 0.8333

Press the CPT key and PMT to compute the amount of monthly deposit.

The value obtained is 442.38.

Therefore, Mike will have to deposit $442.38 every month to reach his goal.

b. The monthly interest rate is calculated by entering the below in a financial calculator:

FV= 1,000,000

N= 360

PMT= -350

Press the CPT key and I/Y to compute the monthly interest rate.

The value obtained is 0.9238.

Therefore, the annual interest rate is 0.9238%*12= 11.0852%   11.09%.

c.Effective annual rate is calculated using the below formula:

EAR= (1+r/n)^n-1

Where r is the interest rate and n is the number of compounding periods in one year.

EAR= (1+0.11/365)^365-1

        = 1.1163 – 1

        = 0.1163*100

        = 11.63%.