Fred borrowed money 18 months ago at 12% compounded semi-annually. He now owes a total of $5,450. How much of this is interest?
A) $874.07
B) $893.71
C) $767.67
D) $3,540.63
E) $1,041.04

Question

Quizplus · Accepted Answer

The interest can be calculated using the formula for compound interest: A = P(1 + r/n)^(nt), where A is the amount owed, P is the principal amount (initial investment), r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the time the money is invested for in years. Here, A = $5,450, r = 12% or 0.12, n = 2 (since the interest is compounded semi-annually), and t = 1.5 years (18 months). Rearranging the formula to solve for P gives P = A / (1 + r/n)^(nt). Substituting the given values and solving for P gives the initial amount borrowed. The interest is then A - P. Calculating this gives an interest amount of approximately $874.07.

Fred Borrowed Money 18 Months Ago at 12% Compounded Semi-Annually