A contract stipulated a payment of $8,500 plus 6.4% interest compounded monthly in 30 months. Prior to the due date, the contract was sold for $9,700 based on 3.8% interest compounded quarterly. How many months before maturity did the contract change hands?
A) 9 months and 22 days
B) 8 months and 22 days
C) 7 months and 22 days
D) 6 months and 22 days
E) 5 months and 22 days

Question

Quizplus · Accepted Answer

The future value (FV) of the contract at maturity can be calculated using the formula for compound interest: $FV = P(1 + \frac{r}{n})^{nt}$, where $P$ is the principal amount, $r$ is the annual interest rate, $n$ is the number of times the interest is compounded per year, and $t$ is the time in years. For the original contract, $P = \$8,500$, $r = 6.4\%$, $n = 12$ (since it's compounded monthly), and $t = 2.5$ years (30 months). Plugging these values into the formula gives the future value at maturity.When the contract is sold, it's based on a 3.8% interest rate compounded quarterly ($n = 4$). To find out how many months before maturity the contract was sold, we need to calculate the present value (PV) of the contract at the sale point using the future value we found for the maturity, with the new interest rate and compounding frequency. The formula rearranges to solve for $t$, the time from the sale to maturity, given the sale price ($PV = \$9,700$) as the present value now.Solving these equations gives us the time from the sale to maturity. Subtracting this time from the total maturity period (30 months) gives the time at which the contract was sold before maturity. The correct calculation leads to approximately 8 months and 22 days before maturity, which corresponds to choice B.

A Contract Stipulated a Payment of $8,500 Plus 6