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 20 years. What is the annual payment you expect to receive beginning in year 11
if you assume an interest rate of 8 percent for the whole time period? (Do not round
intermediate calculations. Round your answer to 2 decimal places. (e.g., 32.16))

Answer 1

To calculate the annual payment you can expect to receive beginning in year 11 from the life insurance fund, use the present value formula for an ordinary annuity. The annual payment is approximately $870.09.

Step-by-step explanation:

To calculate the annual payment you can expect to receive beginning in year 11, you need to calculate the present value of the annuity. The present value formula for an ordinary annuity is:

PV = C * [(1 - (1 + r)^-n) / r]

Where PV is the present value, C is the annual payment, r is the interest rate per period, and n is the number of periods.

In this case, the annual payment is unknown, the interest rate is 8%, and the number of periods is 20. We need to find the present value, which is $10,000. By rearranging the formula and plugging in the given values, we can solve for C:

C = PV * [r / (1 - (1 + r)^-n)]

Using the given values:

C = 10000 * [0.08 / (1 - (1 + 0.08)^-20)]

Calculating this expression, we find that the annual payment you can expect to receive beginning in year 11 is approximately $870.09.