Upon graduation from college, Kelly was able to defer...

Upon graduation from college, Kelly was able to defer payment on his $40,000 subsidized Stafford student loan for 6 months. Since the interest will no longer be paid on his behalf, it will be added to the principal until payments begin. If the interest is 6.54% compounded monthly, what will the principal amount be when he must begin repaying his loan? Source: SallieMae.

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Key Concepts

Interest Rate Conversion

Interest rate conversion is the process of converting an annual interest rate to a periodic rate that matches the compounding period. In the case of monthly compounding, the annual rate is divided by 12 to determine the rate applied each month, ensuring accurate calculation of interest over shorter periods.

Deferred Payment and Capitalization

Deferred payment in the context of loans refers to postponing scheduled payments, during which interest may continue to accrue. When the accrued interest is added to the principal—a process known as capitalization—the borrower ends up with a higher principal balance on which future interest is calculated.

Compound Interest

Compound interest is the process where interest is added to the initial principal, and then future interest accrues on the increased principal amount. This results in interest being earned on previously accumulated interest as well as on the original investment or loan.

Monthly Compounding

Monthly compounding refers to the calculation of interest on a monthly basis. Here, the annual interest rate is divided by 12, and interest is computed and added to the principal each month, resulting in a more rapid increase in the overall balance compared to less frequent compounding intervals.

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