A person owes $4000 ten (10)months from now.It is agreed that she can,instead,pay $X now and another $2000 two years from now to replace the given debts.If simple interest is r = 9%,what is X using 8 months as the focal date?
A)$1929.20
B)$2026.02
C)$2033.18
D)$2155.17

Question

Quizplus · Accepted Answer

The correct answer is found by calculating the present value of both payments at the 8-month focal date, using the formula for present value with simple interest: $PV = \frac{FV}{(1 + rt)}$, where $PV$ is the present value, $FV$ is the future value, $r$ is the annual interest rate, and $t$ is the time in years. For the $4000 due in 10 months, since the focal date is 8 months before, it is due in 2 months or $\frac{2}{12}$ years from the focal date. For the $2000 due in 2 years, since the focal date is 8 months before, it is due in 2 years and 8 months or $\frac{32}{12}$ years from the focal date. Calculating the present value of both amounts and solving for $X$ gives the correct answer.

A Person Owes $4000 Ten (10)months from Now