Amortization Schedules: Principal vs. Interest Over Time

What is an amortization schedule?

An amortization schedule breaks each monthly loan payment into two components:

• Interest on the current outstanding balance,
• Principal — what's left over, which pays down the balance.

Early payments are mostly interest; late payments are mostly principal. The monthly payment stays constant.

The monthly payment formula

$PMT = P \cdot \dfrac{r(1 + r)^n}{(1 + r)^n - 1}$

where $P$ = loan principal, $r$ = periodic rate, $n$ = total number of payments.

Step-by-step solution

Setup: $P = 200{,}000$, annual rate 4% ⟹ $r = 0.04/12 \approx 0.003333$, term 30 years ⟹ $n = 360$ months.

Step 1 — Compute $(1 + r)^n$: $(1.003333)^{360} \approx 3.31349$

Step 2 — Plug into the formula: $PMT = 200{,}000 \cdot \dfrac{0.003333 \cdot 3.31349}{3.31349 - 1} = 200{,}000 \cdot \dfrac{0.011045}{2.31349}$

Step 3 — Divide and multiply: $PMT \approx 200{,}000 \cdot 0.004774 \approx \boxed{954.83}$

The monthly payment is about $954.83.

Month-by-month breakdown

For each month $k$:

• $\text{Interest}_k = B_{k-1} \cdot r$ (interest on prior balance)
• $\text{Principal}_k = PMT - \text{Interest}_k$
• $B_k = B_{k-1} - \text{Principal}_k$

Month 1:

• Interest = $200{,}000 \cdot 0.003333 = 666.67$
• Principal = $954.83 - 666.67 = 288.17$
• New balance = $199{,}711.83$

Month 180 (halfway):

• Outstanding balance ≈ $125{,}560
• Interest ≈ $418.53, Principal ≈$536.30 — crossover to mostly principal

Month 360 (last payment):

• Interest ≈ $3.17, Principal ≈$951.66 — nearly all principal

Total interest paid

$\text{Total paid} = 360 \cdot 954.83 \approx 343{,}739$ $\text{Interest} = 343{,}739 - 200{,}000 \approx 143{,}739$

On a 4% 30-year mortgage, you pay about 72% of the original loan amount in interest. Shorter terms or higher prepayments shrink this dramatically.

Why payments are interest-heavy early

Because interest = rate × balance, and the balance is largest at the start. Each payment that eats even a little principal shrinks the interest on all future payments — compounding in reverse.

Common mistakes

• Using the annual rate as $r$ in the monthly payment formula.
• Forgetting $n$ is months, not years.
• Assuming half of all payments is half the principal paid. By month 180 (halfway through), you've still paid off only about 37% of the principal.

Try it in the visualization

A stacked area chart shows interest (warm color) shrinking and principal (cool color) growing as the month counter advances, while the outstanding balance curves down to zero.