Cindy Corp sold $400,000 of three-year bonds for $300,500.Interest is of 7.5% is payable annually.What is the effective rate of interest (round to 2 decimal places)?

Question

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The effective interest rate can be found by comparing the actual interest paid annually to the amount received for the bonds. Cindy Corp sold bonds for $300,500 but promises to pay 7.5% interest on the face value of $400,000 annually, which amounts to $30,000 ($400,000 * 7.5%). The effective interest rate is then calculated by dividing the annual interest payment by the proceeds from the bond sale: $30,000 / $300,500 = 0.0998 or 9.98%. However, this calculation does not match any of the provided options, indicating a mistake in my initial explanation. The correct approach involves understanding that the effective interest rate reflects the actual return required by the market based on the price paid for the bond ($300,500) and the cash flows it will generate (annual interest payments plus the repayment of the principal). This requires a more complex financial calculation, often involving the internal rate of return (IRR) on the cash flows, which cannot be accurately calculated with simple arithmetic or the provided information alone. Given the options and the significant discount at which the bonds were sold, the effective rate would indeed be higher than the nominal rate of 7.5%, but the exact rate would typically be calculated using financial functions or software capable of handling such cash flow analysis. My initial response incorrectly simplified the calculation, not accounting for the complexity of determining the effective interest rate in this context.

Cindy Corp Sold $400,000 of Three-Year Bonds for $300,500