Calculate the accumulated value after twenty years of payments of $12 000.00 made at the end of each year if interest is 6% compounded semi-annually.

Question

Quizplus · Accepted Answer

The correct calculation involves using the formula for the future value of an annuity, which accounts for regular payments (PMT) made at the end of each period and the compounding interest rate. Given that the interest is compounded semi-annually but payments are made annually, we adjust the interest rate for the annual payments. The formula for the future value of an annuity is FV = PMT * [((1 + r)^n - 1) / r], where PMT is the annual payment, r is the annual interest rate (expressed as a decimal), and n is the total number of payments. Here, PMT = $12,000, r = 6% or 0.06 (annual interest rate), and n = 20 (years). However, because the interest is compounded semi-annually, we use the effective annual rate (EAR) for the calculation, which still aligns with the formula since payments are annual. Plugging the values into the formula or using a financial calculator with these inputs gives us the future value closest to choice A, $445,721.73.

Calculate the Accumulated Value After Twenty Years of Payments of $12