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Chapter 8: Problem 35

To borrow money, you pawn your guitar. Based on the value of the guitar, the pawnbroker loans you \(\$ 960\). One month later, you get the guitar back by paying the pawnbroker \(\$ 1472\). What annual interest rate did you pay?

Short Answer

Expert verified
The annual interest rate paid was 6.4 or 640%.

Step by step solution

01

Calculate the One Month Interest Rate

First, find the total interest paid by subtracting the loan amount from the repayment amount. The formula to calculate this is: Interest = Repayment amount - Loan amount. Substituting our values it would be: Interest = \$1472 - \$960 = \$512. Then, divide the interest by the loan amount to get the one-month interest rate. Interest rate (one month) = Interest / Loan amount. This would be: Interest Rate (one month) = \$512 / \$960 = 0.53333333.
02

Annualize the Interest Rate

Next, multiply the one-month interest rate by 12 to get the annual interest rate. Use the formula: Annual Interest Rate = Monthly Interest Rate * 12. Substituting our value, it would be: Annual Interest Rate = 0.53333333 * 12 = 6.4 (or 640% when represented as a percentage).

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