Question

Find the annual simple interest rate of a loan, where $900 is borrowed and $936 is repaid at the end of 4 months. (Answer in percent)

A) 6%
B) 7.5%
C) 9%
D) 12%

Answer 1

To calculate the annual simple interest rate of the loan, we find the interest earned ($36), convert the loan period to years (1/3 year), and rearrange the formula I = PRT to solve for R, resulting in an annual interest rate of 12%.

Step-by-step explanation:

To find the annual simple interest rate for the given loan, we use the formula for simple interest I = PRT, where I is the interest, P is the principal, R is the interest rate per period, and T is the number of periods.

First, we determine the interest earned on the loan:

• Interest (I) = Total repayment - Principal borrowed
• Interest (I) = $936 - $900 = $36

Since the loan period is for 4 months, we convert this to a fraction of a year by dividing by 12 (months in a year):

• T (in years) = 4 months ÷ 12 months/year = 1/3 year

Then, we rearrange the simple interest formula to solve for the annual interest rate (R):

• R = I ÷ (P × T)
• R = $36 ÷ ($900 × 1/3)
• R = $36 ÷ $300
• R = 0.12 or 12%

Therefore, the annual simple interest rate is 12%, which corresponds to answer choice D).