Suppose you run an insurance company that sells annuities. A customer comes in who wants to buy an annuity that will provide a monthly payment of $2000 for 20 years. The relevant annual interest rate is 6%. How much will you charge for this annuity contract

Amount charged for this annuity contract = $279,161.54

Step-by-step explanation

Amount charged for this annuity contract = present value of the monthly payment

Assuming that the payment is made at the end of each month, then;

Present value = A * {1 - (1 + r) ^{- n}}/ r

Where;

A - Monthly payment

r- Interest rate

n- Time

A = 2,000, r = 6%/ 12 = 0.5% and n = 20 * 12 = 240

Amount charged = 2,000 * {1 - (1.005) ^{- 240}}/ 0.005

             = 2,000 * 139.580772

             = $279,161.54