Question

An insurance company is trying to sell you a retirement annuity The annuity will give you 20 payments with the first payment in 12 years when you retire. The insurance firm is asking you to pay $50,000 today. If this is a fair deal, what must the payment amount be (to the dollar) if the interest rate is 8 percent?

Answer 1

Answer:

$11,874.13

Explanation:

Data provided in the question:

Present value = $50,000

Number of payments, m = 20

Since the first payments is given in 12 years, therefore

number of interest periods, n = 11

Interest rate, r = 8% = 0.08

Now,

Future value = Present value × ( 1 + r)ⁿ

= $50,000 × ( 1 + 0.08)¹¹

= $116,581.95

Thus,

Payments = Future value × $\frac{r}{1-(1+r)^{-m}}$

thus,

Payments = $116,581.95 × $\frac{0.08}{1-(1+0.08)^{-20}}$  

= $116,581.95 × 0.1018522

= $11,874.13