Your uncle promises to give you $550 per quarter for the next five years starting today . How much is his promise worth right now if the interest rate is 8% compounded quarterly?

Question

Quizplus · Accepted Answer

The promise is worth $9,173.14 today, calculated using the present value of an annuity formula since the payments are made at the beginning of each period (annuity due). The formula for the present value of an annuity due is $PV = P \times \left[\frac{1 - (1 + r)^{-n}}{r}\right] \times (1+r)$, where P is the payment amount, r is the interest rate per period, and n is the total number of payments. Here, P = $550, r = 0.08/4 = 0.02 (quarterly interest rate), and n = 5*4 = 20 (total quarters). Plugging these values into the formula gives the present value as $9,173.14.

Your Uncle Promises to Give You $550 Per Quarter for the Next