Question

How much should Liz's dad invest into a savings account today, to be able to pay for Liz's rent for the next 6 years if rent is $650 payable at the beginning of each month? The savings account earns 3.4% compounded monthly. Round to the nearest cent

Answer 1

Given: Liz's rent per month is $650. The savings account compound interest is 3.4% per month. Liz's have to pay the rent for 6 years. Therefore, the total rent amount is, 12 x 6 x 650 = 72 x 650 = $46,800 The formula for compound interest is, 71 7 A = P 1+ where A is the final amount, P is an initial principal amount, r interest n rate, n is the number of times interest applied per time period and t is the number of time period. Here, A = 46,800, P = ?, n =12, t=6 and r =0.034.

Substitute the above values in the compound interest formula, 12x6 0.034 46800 = P 1+ 12 72 46800 = P 12.034 12 72 72 12 P= 46800 12.034 P - 46800x(0.997) P = 46800 x 0.8172 P 38244.96 Hence, Liz's father has to invest into the savings account is $38,244.96.