Short Answer 
The answer explains compound interest as interest calculated on both the principal and accumulated interest, using key components like principal amount, interest rate, and time period. It provides the formula for calculating compound interest, especially for loans compounded monthly, and demonstrates its application with an example of an Unsubsidized Stafford Loan, resulting in a final repayment amount of $5,467.
Step 1: Understanding Compound Interest
Compound interest is the process where borrowers must pay interest on both the original principal and on the accumulated interest from previous periods. This leads to a situation where the amount owed can grow significantly over time. Key components of compound interest include:
- P – the initial principal amount.
- r – the interest rate, expressed as a percentage.
- n – the number of time periods, usually in years, that the money is invested or borrowed.
Step 2: Using the Compound Interest Formula
The formula to calculate compound interest is essential for understanding how much you will owe. The basic compound interest formula is:
A = P(1 + r/100)^n
For loans compounded monthly, it is modified to:
A = P(1 + (r/12)/100)^(12*n)
This formula allows you to account for the monthly compounding, which results in a higher total amount at repayment.
Step 3: Calculating the Final Amount for Stafford Loan
To find the total amount owed on an Unsubsidized Stafford Loan, you put the principal and rate into the formula. For example, if the principal is $4,980, and the annual interest rate is 6.25%, you would use:
A = 4980(1 + (6.25/12/100))^(12*1.5)
This will yield:
- Calculate the monthly rate: r/12/100 = 0.0052
- Apply it to the formula: A = 4980(1 + 0.0052)^(18)
- Final amount: A = $5,467
The result shows that the higher balance due to compound interest results in a total repayment amount of $5,467.