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Amortization

Amortization is the process of paying off a loan through regular, equal payments over a set period. Each payment covers some interest and some of the original amount borrowed (the principal), with the interest portion shrinking and the principal portion growing as time goes on.

Amortization is a method of debt repayment in which a borrower makes periodic fixed payments, each consisting of an interest component and a principal component. The interest portion of each payment is calculated on the remaining balance, so early payments are interest-heavy while later payments apply more toward reducing the principal. The fixed payment amount is determined by a formula that accounts for the loan amount, periodic interest rate, and total number of payments.

Key Formula

M=P⋅r(1+r)n(1+r)n−1M = P \cdot \frac{r(1 + r)^n}{(1 + r)^n - 1}
Where:
  • MM = the fixed monthly payment
  • PP = the principal (original loan amount)
  • rr = the monthly interest rate (annual rate ÷ 12)
  • nn = the total number of payments

Worked Example

Problem: You borrow $12,000 at an annual interest rate of 6%, to be repaid in equal monthly payments over 2 years. What is the monthly payment, and how much of the first payment goes toward interest versus principal?
Step 1: Identify the values. The principal is $12,000, the annual rate is 6%, and the loan term is 2 years.
P=12,000,r=0.0612=0.005,n=2×12=24P = 12{,}000, \quad r = \frac{0.06}{12} = 0.005, \quad n = 2 \times 12 = 24
Step 2: Calculate (1+r)n(1 + r)^n.
(1.005)24≈1.12716(1.005)^{24} \approx 1.12716
Step 3: Plug the values into the amortization formula.
M=12,000⋅0.005×1.127161.12716−1=12,000⋅0.0056360.12716≈531.84M = 12{,}000 \cdot \frac{0.005 \times 1.12716}{1.12716 - 1} = 12{,}000 \cdot \frac{0.005636}{0.12716} \approx 531.84
Step 4: Find the interest portion of the first payment by multiplying the full balance by the monthly rate.
Interest1=12,000×0.005=60.00\text{Interest}_1 = 12{,}000 \times 0.005 = 60.00
Step 5: Subtract the interest from the payment to find the principal portion.
Principal1=531.84−60.00=471.84\text{Principal}_1 = 531.84 - 60.00 = 471.84
Answer: The monthly payment is approximately 531.84.Ofthefirstpayment,531.84. Of the first payment,60.00 goes toward interest and $471.84 goes toward reducing the principal.

Visualization

Why It Matters

Amortization is the structure behind most car loans, mortgages, and student loans. Understanding it reveals why you pay so much interest early in a loan and helps you evaluate whether extra payments or refinancing could save you money. Financial literacy around amortization is essential for making informed borrowing decisions.

Common Mistakes

Mistake: Using the annual interest rate directly in the formula instead of converting to the monthly rate.
Correction: Divide the annual rate by 12 to get the monthly rate. For example, a 6% annual rate becomes 0.06 ÷ 12 = 0.005 per month.
Mistake: Assuming each payment splits evenly between interest and principal.
Correction: The split changes with every payment. Early payments are mostly interest; later payments are mostly principal, because interest is always calculated on the remaining balance.

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