Fred borrowed money 18 months ago at 12% compounded semiannually. He now owes a total of $5450. How much of this is interest?
A) $874.07
B) $893.71
C) $767.67
D) $3540.63
E) $1041.04

Question

Quizplus · Accepted Answer

The formula for compound interest is $A = P(1 + \frac{r}{n})^{nt}$, where $A$ is the amount of money accumulated after n years, including interest, $P$ is the principal amount (the initial amount of money), $r$ is the annual interest rate (decimal), $n$ is the number of times that interest is compounded per year, and $t$ is the time the money is invested or borrowed for, in years. Given that the interest rate is 12% or 0.12 as a decimal, compounded semiannually ($n = 2$), over a period of 18 months (or 1.5 years), and the final amount is $5450, we need to find the initial principal $P$. Rearranging the formula to solve for $P$ gives $P = \frac{A}{(1 + \frac{r}{n})^{nt}}$. Substituting the given values: $P = \frac{5450}{(1 + \frac{0.12}{2})^{2 \times 1.5}}$, calculating this gives $P = 4575.93$. The interest is the difference between the final amount and the principal: $5450 - $4575.93 = $874.07.

Fred Borrowed Money 18 Months Ago at 12% Compounded Semiannually