A student takes out a college loan of 10,000 at an annual...

A student takes out a college loan of $\$ 10,000$ at an annual percentage rate of 6$\%$ , compounded monthly.
a. If the student makes payments of $\$ 100$ per month, how much does the student owe after 12 months?
b. After how many months will the loan be paid off?

Key Concepts

Loan Payment and Outstanding Balance Calculation

Calculating the outstanding balance of a loan with periodic payments involves combining the compounded growth of the principal with the reduction caused by each payment made. This requires an understanding of how each payment affects the remaining balance, taking into account both the accrual of interest and the repayments over time.

Amortization

Amortization is the process of spreading out a loan into a series of fixed periodic payments over time. These payments cover both principal and interest, gradually reducing the outstanding balance until the loan is completely paid off. Understanding amortization is key to managing loans and planning repayment schedules.

Periodic (Monthly) Compounding

Monthly compounding refers to the calculation of interest on a loan or investment on a monthly basis. This means that the interest accrued is added to the principal every month, increasing the base amount on which subsequent interest is calculated. It is an important detail when determining the total cost or return of a financial product over a given time period.

Compound Interest

Compound interest is the process by which interest is earned on both the initial principal and the accumulated interest from previous periods. It means that the growth of the amount owed or invested increases exponentially over time, rather than linearly, and is a fundamental concept in financial calculations involving loans, investments, and savings.

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