Question

Consider a retirement plan that pays 50000 a year for 15 years. The interest rate in the economy is 4%.

a. What is (actuarilly fair) price of the retirement plan?

b. If instead of the retirement plan you wish to put your money in a savings account that pays you 3% annually, how much money would you need to have saved at retirement to get

the same payment as with the retirement plan?

c.Imagine that the plan has a clause that allows you to do the following: after 10 payments have been made, you can either continue with the plan or abandon the plan and get a single lump sum payment in the date the 11th payment is due.

What is the maximum possible value of the single payment?

Answer 1

(a) Fair Price of retirement plan will be the present value of the annual payments for the 15 years.

Price of retirement plan = $50,000 * Annuity of 4% for 15 years

= $50,000 * 11.118387

= $555,919.35

(b) Investment in savings account will be equal to the present value of expected payments

Investment in Savings account = Annual Payments * Annuity of 3% for 15 years

= $50,000 * 11.937935

= $596,896.75

(c) Maximum value of 11th single payment will be the present value of all future payments to be received from retirement plan

Maximum value of 11th single payment = value of 11th payment + present value of 4 future payments

= $50,000 + ($50,000 * Annuity of 4% for 4 years)

= $50,000 + ($50,000 * 3.629895)

= $50,000 + $181,494.75

= $231,494.75

Note: The present value factors are rounded off to 6 decimal places for calculation. If your question provides for present value factors, then please use the provided ones as it can result in rounding off differences.