Question

You deposit $10,000 annually into a life insurance fund for the next 10 years, at which time you plan to retire. Instead of a lump sum, you wish to receive annuities for the next 25 years. What is the annual payment you expect to receive beginning in year 15 if you assume an interest rate of 4 percent for the whole time period? (Show you work and calculations)

Answer 1

The accumulated value of funds deposited in first 10 year must be equal to the present value of annuities receive in next 25 years.

The accumulated value of deposits after 10 year is calculated below:

The above calculated accumulated value must be compounded for next 4 year to get value at the beginning of 15 year.

Now, the below expression can be used to calculate the annual receives:

Substitute the calculated accumulated value for present value, 0.04 for i​​​​​​ and 25 for n,

Thus, individual will receive $8,644.97 every year for 25 years.