The loan payment
A fixed-rate loan with equal payments uses the amortisation formula
M = P × r ÷ (1 − (1 + r)⁻ⁿ), where P is the principal, r the
monthly interest rate (annual ÷ 12) and n the number of monthly payments. The payment is
constant; what changes is the split. Early payments are mostly interest because the balance is large,
and the principal share grows as the balance falls.
Measured with the calculator on this site: 200,000 at 6% over 30 years gives a monthly payment of 1,199.10, total payments of 431,676.38 and total interest of 231,676.38. The first payment splits into 1,000.00 of interest and 199.10 of principal; the last is almost all principal. That shape is why paying extra early saves more than paying the same amount late: it removes interest from every subsequent month.
Compound growth with contributions
Compound interest on a lump sum is P × (1 + r)ⁿ. With monthly contributions it is a
future-value annuity: the balance grows at the monthly rate and the contribution is added each month.
Measured: 10,000 at 4% with 200 a month for five years ends at 25,469.76, of which
22,000 is contributions and 3,469.76 is interest. The year-by-year table is the useful part — the
interest in year one is small, and it grows because it is a percentage of a larger balance.
The rate convention matters. A nominal 4% applied monthly is about 4.07% effective; a loan quoted at 6% with monthly compounding is not the same as 6% simple interest. The calculator states that it applies the annual rate divided by twelve, which is the common convention for consumer products.
Snowball and avalanche
A payoff plan takes the minimum payments and puts the extra money on one debt at a time. Snowball targets the smallest balance first; avalanche targets the highest interest rate. The measured example: a 3,000 balance at 5% and an 8,000 balance at 22%, minimums 100 and 200, with 150 extra a month. Snowball clears in 32 months with 3,250.57 of interest; avalanche clears in 31 months with 2,673.87 — 576.70 less and one month sooner.
Avalanche is the mathematically cheaper order whenever the highest-rate debt is not the smallest. The case for snowball is behavioural: clearing a small balance early gives a visible win, and a plan someone follows beats an optimal plan they abandon. The calculator shows both side by side so the trade-off is explicit rather than argued.
What an extra payment does
An extra payment goes entirely to principal, so it removes interest from every remaining month. On the 200,000 loan above, paying 200 extra a month shortens the term and cuts the total interest by far more than 200 × the number of months, because the saved interest compounds. The exact saving depends on when the extra payments start: a lump sum in year one is worth more than the same total spread over year twenty, because every month it is not on the balance is a month of interest avoided.
Which rate is being quoted?
A loan quote can use an APR, a nominal annual rate, or a monthly rate, and the difference is not cosmetic. The formula here takes the annual rate and divides by twelve; if the lender quotes a monthly rate, multiply by twelve before entering it, or the payment will be wrong by an order of magnitude. APR also folds in some fees, while a nominal rate does not, so two “6%” loans can cost different amounts. Compare the total repayment or the APR, not the headline number.
For savings and investments, the same split appears as nominal versus effective. A 4% nominal rate compounded monthly is about 4.07% effective; a rate advertised as effective already includes the compounding. Enter the convention the product uses, and state it when you compare two projections.
Mistakes that change the answer
- Using the annual rate as the monthly rate. Divide by twelve before applying the formula; using 6 instead of 0.5 makes the payment absurdly large.
- Ignoring fees and insurance. A quoted payment may exclude arrangement fees, payment protection or taxes; the amortisation schedule covers principal and interest only.
- Comparing total interest across different terms. A longer term lowers the payment and raises the total interest; both are true, and the comparison has to say which one matters.
- Treating a minimum payment as a payoff plan. Minimums on a high-rate card can take decades; the extra amount is what determines the end date.
- Assuming a savings rate is fixed. A long projection at one rate is a scenario, not a promise; rerun it lower to see the range.