Asked by Morgan Rivers on May 11, 2024

verifed

Verified

Laurel borrowed some money from Hardy 42 months ago. The loan principal plus interest at 17% compounded annually is to be repaid today. Laurel and Hardy agree that the total amount due is $31,618. How much did Laurel borrow from Hardy 42 months ago?

A) $10,618.49
B) $13,367.12
C) $18,250.88
D) $23,157.32
E) $49,868.89

Compounded Annually

Interest on an investment that is calculated once a year, where the interest earned each year is added to the principal.

Loan Principal

The initial amount of money borrowed in a loan, excluding interest and other charges.

42 Months

A time period equal to three and a half years.

  • Put into practice financial operations to solve difficulties pertaining to investments and loans.
verifed

Verified Answer

FC
Florita CardozaMay 14, 2024
Final Answer :
C
Explanation :
The formula for compound interest is A = P(1 + 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. In this case, A = $31,618, r = 17% or 0.17, n = 1 (since the interest is compounded annually), and t = 42 months or 3.5 years. We need to solve for P. Rearranging the formula to solve for P gives us P = A / (1 + r/n)^(nt). Substituting the given values, we get P = $31,618 / (1 + 0.17/1)^(1*3.5) = $31,618 / (1.17)^3.5 ≈ $18,250.88.