Question

Holly Krech is planning for her retirement, so she is setting up a payout annuity with her bank. She wishes to receive a payout of $1,900 per month for twenty years.

(a) How much money must she deposit if her money earns 7.8% interest compounded monthly? (Round your answer to the nearest cent.)

(b) Find the total amount that Holly will receive from her payout annuity.

Answer 1

The formula for annuity payments of $ P per month for n months is P = r(PV)/[1-(1+r)^-n] where r is the interest rate per period and PV is the present value of the deposit.

Here, P = $ 1900, r = 7.8/1200 = 0.0065 and n = 20*12 = 240.

(a). As per the above formula, the amount that Holly Krech must deposit is PV = (P/r) [1-(1+r)^-n] = (1900/0.0065)[1- 1/(1.0065)²⁴⁰] = (1900/0.0065)(1-0.211199548) = (1900/0.0065)(0.788800451) = $ 230572.44 ( on rounding off to the nearest cent). Thus, Holly Krech must deposit $ $ 230572.44 in order to receive a payout of $1,900 per month for twenty years.

b). The total amount that Holly will receive from her payout annuity is 240*$ 1900 = $ 456000.