The maturity value of a 4-month loan of $5,250 is $5,361.50. What is the annual simple interest rate (in percent) on this loan? (Round your answer to one decimal place.)

Question

The maturity value of a 4-month loan of $5,250 is $5,361.50. What is the annual simple interest rate (in percent) on this loan? (Round your answer to one decimal place.)

Show your work

Answer 1

To calculate the annual simple interest rate, we first need to find the simple interest earned on the loan.

Simple Interest = Maturity Value - Principal
Simple Interest = $5,361.50 - $5,250
Simple Interest = $111.50

Next, we need to find the simple interest rate for 4 months and then convert it to an annual rate.

Simple Interest Rate for 4 Months = (Simple Interest / Principal) * (12 / 4)
Simple Interest Rate for 4 Months = ($111.50 / $5,250) * (12 / 4)
Simple Interest Rate for 4 Months = 0.02119

Finally, to find the annual simple interest rate, we multiply the 4-month rate by 3 to convert it to a yearly rate.

Annual Simple Interest Rate = 0.02119 * 3 * 100
Annual Simple Interest Rate = 6.36%

Therefore, the annual simple interest rate on this loan is 6.4%.

Answer 2

in the last step, why do you multiply by 3?

Answer 3

We multiply by 3 because we are converting the interest rate from a 4-month rate to an annual rate. Since there are 12 months in a year, we need to multiply the 4-month rate by 3 to get the annual rate. This is done because the 4-month rate represents one-third of a year, so multiplying by 3 gives us the equivalent annual rate.