Question

why do we have to multiply the futuce value of the annuity twice? i understand how they got up to 5,095 times the future value of the annuity but am lost after that.

4. An insurance company has an obligation to pay medical bills for a claimant. Average annual claims costs today are $5,000, and medical inflation is expected to be 7% per year. The claimant is expected to live an additional 20 years. Claim payments are made at yearly intervals, with the first claim payment to be made one year from today. Find the present value of the obligation if the annual interest rate is 5%. (A) 87,932 (B) 102,514 (C) 114,611 (D) 122,634 (E) Cannot be determined Assuming the claimant survives exactly the expected 20 years, his payments will be 5000(1.07), 5000 (1.07),..., 5000 (1.07). The PV of these payments at 5% is 1.07 1.072 1.0720 ] 5000-1.07.1.07 1.07 500 1.05 * 1,057 +21.05 ) S1.050 ++ |(1,07 5000.1.07/1.05 1.051.07 (1.05) 5000-1.07 1.45844_5000-1.07-0.458443 = 122,634 1.65 0.02 0.02 1.05 Alternatively: 1.07 -1.01905, Los =1.01905 5000-1.07 1.05 - Szalo1905 = 5,095.238 - Solo1905 = 122,634Szalo1905 = 122,634 Answer:D

Answer 1

The face value is not multiplied by annuity twice.

Here in the solution given , the equation goes like this

5000*1.07/1.05* s20]0.019050

5095.2538 is the solution to 5000*1.07/1.05 this part

And it is the present value of the payment received after year value , not the 20 years future value.

So we need to calculate the present value of all the years and so the second part is multiplied by 5095.2538.

And so the Present value of annuity of 20 years is multiplied by 5095.2538 to get $12264.