Question

Mark is planning to retire in 30 years. he wishes to make monthly deposits in a retirement fund until he retires so that, beginning one-year following his retirement, he will receive annual payments of $100,000 for the next 25 years. The interest rate is 10% compounded daily. Assume 30 days per month and 365 days per year.

a. What is the effective monthly interest rate?

b. What is the effective annual interest rate?

c. How much money must he have in his savings account at retirement?

d. How much money must he deposit every month for the next 30 years?

Answer 1

I = 10% compounded daily

a) effective rate monthly= (1+0.1/365)^30 - 1

= 0.00825191

= 0.825191%

b) effective rate yearly= (1+0.1/365)^365 - 1

= 0.10515578

= 10.515578 %

c ) Here he wishes to withdraw 100000 for 25 years after retirement, we have to find present value of this annuity series at the retirement

P = A (P/A,10.5155%,25)

= 100000*8.7288296

= 872882.96

d) Future value of retirement fund at retirement is calculated above

We need to find monthly annuity to reach that future value

A = F *(A/F, 0.825191%, 360)

= 872882.96 * 0.000451689

= 394.27