Question

Assume that Quick Insurance is required to pay the health care costs of an insured individual

with an initial annual amount of $8,000 to be paid today. The individual is also expected to

receive additional payments at the end of the next 18 years from Quick Insurance where each

additional payment increases by 6% each year due to inflation of medical costs (including the

first year, so the end of the 1st year payment will be $8,000 x 1.06). (a) What is the last payment

in year 18? (b) Calculate the present value obligation today, including today’s payment, if the

annual interest rate is 4%? Please show formulas. Do not use Excel. Can use HP 10bll+ calculator.

Answer 1

a) The last payment in the year 18 = $8000 *1.06^18 = $22834.71

b) Present value of obligation = present value of all the payments including today's payments (19 payments)

= 8000+ 8000*1.06/1.04 + 8000*1.06^2/1.04^2+.....+8000*1.06^18/1.04^18

Using the Sum of GP formula

=8000*((1.06/1.04)^19-1)/(1.06/1.04-1)

=181408.40

Thus, the present value of obligation (including today's payment) = $181408.40