A $6300 face-value investment earning interest at 10% compounded annually for a six-year term was sold for $7550. How many years before its maturity date was the note sold if it was discounted to yield 12% compounded monthly?
A) 2.73
B) 3.27
C) 4.50
D) 12.38
E) 39.28

Question

Quizplus · Accepted Answer

The note was sold 3.27 years before its maturity date. To find this, first calculate the future value of the investment at maturity using the formula for compound interest: FV = PV(1 + r)^n, where FV is the future value, PV is the present value, r is the annual interest rate, and n is the number of years. Here, FV = $6300(1 + 0.10)^6 = $8953.23. Then, to find when the note was sold, use the formula for present value of a future amount discounted at a different rate compounded differently: PV = FV / (1 + r/m)^(mn), where m is the number of compounding periods per year, r is the annual discount rate, and n is the number of years until maturity. Solving $7550 = $8953.23 / (1 + 0.12/12)^(12n) gives n ≈ 3.27 years.

A $6300 Face-Value Investment Earning Interest at 10% Compounded Annually