A woman wants to borrow 12,000 to buy a car. She wants to...

A woman wants to borrow $\$ 12,000$ to buy a car. She wants to repay the loan by monthly installments for 4 years. If the interest rate on this loan is $10 \frac{1}{2} \%$ per year, compounded monthly, what is the amount of each payment?

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Key Concepts

Compound Interest

Compound interest is the process where the interest on a loan or deposit is calculated based on the initial principal and also on the accumulated interest from previous periods. In the context of monthly compounding, the annual interest rate is divided by 12, and interest accrues on the growing balance each month, leading to exponential growth of the payable amount over time.

Annuity

An annuity is a series of equal payments made at regular intervals over a period of time. In financial calculations, it is used to determine the fixed repayment amounts for loans, where each payment covers both the interest accrued during the period and a portion of the principal, ensuring that the loan is fully repaid by the end of its term.

Amortization

Amortization is the process of spreading out a loan into a series of fixed payments over time. The amortization formula combines the principles of compound interest and annuities to calculate how each regular payment will decrease the loan balance, ultimately paying off the entire debt by the final installment.

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