Question

You borrowed $25 from a friend and after 5 months repaid $27. What nominal interest rate didyou pay? What was the effective interest rate?

Answer 1

To calculate the nominal interest rate, we can use the formula:

Nominal Interest Rate = (Total Interest Paid / Initial Amount Borrowed) * (12 / Number of Months)

In this case, the total interest paid is $27 - $25 = $2, the initial amount borrowed is $25, and the number of months is 5. Plugging these values into the formula, we get:

Nominal Interest Rate = ($2 / $25) * (12 / 5) ≈ 19.2%

To calculate the effective interest rate, we use the formula:

Effective Interest Rate = (1 + Nominal Interest Rate/Number of Compounding Periods) ^ Number of Compounding Periods - 1

Since the compounding period is not specified, we’ll assume it to be monthly (12 compounding periods in a year). Plugging in the values, we get:

Effective Interest Rate = (1 + 0.192/12) ^ 12 - 1 ≈ 19.97%

Therefore, the nominal interest rate paid is approximately 19.2%, and the effective interest rate is approximately 19.97%.