Question

Compute the specified quantity. Your total payment on a 5 year loan, which charged 5% annual simple interest, amounted to $40,260. How much did you originally borrow (in dollars)? (Round your answer to the nearest cent.)

Answer 1

To determine how much was originally borrowed on a 5-year loan with 5% simple interest and a total payment of $40,260, you would calculate the principal from the interest formula. The original amount borrowed was $32,208.

Step-by-step explanation:

To determine the original amount borrowed (the principal), we need to understand how simple interest works. Simple interest is given by the formula I = P × r × t, where I represents interest, P is the principal amount, r is the interest rate, and t is the time in years.

In this scenario, the total payment amounts to $40,260 over a 5-year period with a 5% annual interest rate. To find the original loan amount, we first need to calculate the total interest paid over the 5 years. We can do this by rearranging the simple interest formula to solve for P. Let A be the total amount paid back, P the principal, r the interest rate (as a decimal), and t the time in years.

The total amount paid (A) equals the principal (P) plus the interest (I), so:
A = P + I or A = P + (P × r × t)

Substituting the given values, we have:
$40,260 = P + (P × 0.05 × 5)

This simplifies to:
$40,260 = P + (0.25 × P)$40,260 = 1.25P

To find the principal P, we divide both sides of the equation by 1.25:
P = $40,260 / 1.25P = $32,208

Therefore, the original amount borrowed was $32,208.