Loan Interest Calculator

Monthly payment = P × r ÷ (1 − (1 + r)^−n), where r is the annual rate divided by 12 and then by 100, and n is the term in months. Interest in a period = the balance at the start of that period × r. Principal in a period = the payment minus that interest. Total interest = the payments over the whole term minus the principal.

P

Loan amount

a

Annual rate, as a percentage

n

Term in months

r

Monthly rate: the annual rate divided by 12 and then by 100

B

Balance at the start of the period the interest is being charged for

Use it when the interest is the thing you are deciding about — comparing a longer term against a shorter one, or working out what an extra payment would save. Enter the amount, the rate and the term, then read the last four figures as a set rather than the total alone: the first month's interest, the last month's, and the two year totals. The gap between the first and last is the thing that makes prepayment cheap and borrowing long expensive, and it is not visible anywhere in the monthly payment, which is the same in every period. Then compare two terms on the same page, because the first month's interest is identical between them: if the total falls from 318,861.58 to 90,643.89 when you cut the term from 30 years to 10, that entire difference is interest that the shorter version never gets the chance to charge, not interest that was somehow negotiated down.

1. 250,000 at 6.5% over 30 years

   1. Monthly rate: 6.5 ÷ 12 ÷ 100 = 0.00541667
   2. Payment: 250,000 × 0.00541667 ÷ (1 − 1.00541667^−360) = 1,580.17
   3. First month's interest: 250,000 × 0.00541667 = 1,354.17, leaving 226.00 of principal
   4. Last month's interest: the balance is down to about 1,573, so 1,573 × 0.00541667 = 8.52
   5. First year: 16,167.73 of interest out of 18,962.04 paid, so 85.3% of the money went to interest
   6. Last year: 651.11 of interest, and the principal is finally being retired faster than the interest accrues
   7. Total: 568,861.58 paid against 250,000 borrowed, so 318,861.58 is interest

   The default case, and the reference point for the whole page. The payment never changes, and yet the interest inside it falls from 1,354.17 to 8.52 — a factor of about 159 — while the principal inside it rises from 226.00 to about 1,572. That is the entire argument for prepaying early, compressed into two rows of the same schedule.

2. The same loan over 10 years instead of 30

   1. Payment: 250,000 at 6.5% over 120 months = 2,838.70, up from 1,580.17
   2. First month's interest: still 1,354.17 — the balance starts at 250,000 whatever the term is
   3. Total interest: 90,643.89, against 318,861.58 over 30 years
   4. Average interest per year: 9,064.39, against 10,628.72 over 30 years — only 17% lower for a term one third as long
   5. First year: 15,709.59 of interest out of 34,064.40 paid, so 46.1% rather than 85.3%

   Cutting the term by two thirds cuts the interest by more than two thirds — 318,861.58 down to 90,643.89 — and the first month's interest does not move at all. That is the cleanest way to see what the term is actually buying: not a different interest rate, but fewer months in which interest is charged on a balance that has not yet come down. The monthly payment rises by 80% to get there.

3. 100,000 at 12% over 5 years

   1. Payment: 100,000 at 12% over 60 months = 2,224.44
   2. First month's interest: 100,000 × 1% = 1,000.00 exactly
   3. Last month's interest: 22.03, so the ratio is about 45 rather than 159
   4. First year: 11,164.32 of interest out of 26,693.28 paid, which is 41.8%

   A short high-rate loan sits at the other end of the same curve. The interest is still front-loaded, but only by a factor of 45 rather than 159, and the first year sends 41.8% to interest instead of 85.3% — because the principal is being retired fast enough that the balance is meaningfully smaller within the first twelve months. A high rate with a short term looks alarming per month and comparatively harmless in total; the reverse combination is the expensive one.

The rate is fixed for the whole term, so a variable-rate loan is not represented, and on those the split between interest and principal shifts whenever the rate resets rather than following the smooth curve shown here. The model assumes every payment is made on time and in full, with no extra payments, no missed payments, and no fees financed into the balance; an extra payment changes the shape of everything on this page, which is what the extra payment calculator exists for. Years are cut at the twelfth period, so on a term that is not a whole number of years the final year is a stub — at 13 months the second year contains a single period, and its interest is 107.58, which is easy to misread as a monthly figure. In the last period the payment is adjusted to clear the balance exactly, so the interest in that period can be slightly smaller than the period before it; that is a true-up rather than an error. Zero per cent is a valid input rather than a rejected one: every interest figure then comes out as zero and the payment is simply the principal divided by the term, which is the correct answer for a subsidised loan. And no currency is attached to any figure.

How much interest will I pay in total?

On 250,000 at 6.5% over 30 years, 318,861.58 — which is 56.1% of the 568,861.58 you hand over. The same amount over 10 years costs 90,643.89, so the term is doing more work here than the rate is.

Why is the first month's interest so much higher than the last?

Because interest is charged on the balance, and the balance only falls slowly at first. On the default loan the first month is charged on the full 250,000, giving 1,354.17, and the last month is charged on about 1,573, giving 8.52. The payment itself is 1,580.17 in both months; the difference is entirely in how it splits — the amortization schedule at work.

Does the term change the first month's interest?

No, and that is the point worth taking from this page. At 250,000 and 6.5% the first month's interest is 1,354.17 whether the term is 1 month or 30 years, because it depends only on the balance and the rate, and every version starts from the same balance. A shorter term buys you fewer months of interest, not a cheaper month.

What share of my early payments is interest?

On the 30-year loan, 85.3% of everything paid in the first year. Over 10 years it is 46.1%, and on a 5-year loan at 12% it falls to 41.8%. The shorter the term, the faster the balance comes down, and the sooner the split starts favouring principal.

Why does prepaying early save more than prepaying later?

Because an extra payment in year one removes principal that would otherwise have been charged interest for the remaining 29 years, while the same amount paid in year 29 removes principal that was only going to be charged for a few more months. The interest on this loan runs from 1,354.17 in the first month to 8.52 in the last, and that curve is what prepayment is buying back.

What happens at zero per cent?

Nothing degenerate — every interest figure is zero, and the payment is the principal divided by the term: 250,000 over 360 months is 694.44, and the total paid is exactly 250,000. That is the correct answer for a subsidised loan, which is why zero is accepted rather than rejected.

What is not included?

Fees, closing costs, insurance, taxes, any rate resets on a variable-rate loan, and any early repayment. It also assumes every payment is made in full and on time. And no currency is attached to any figure.

• 12 CFR 1026.18 — Content of disclosures (Truth in Lending): the rules for the disclosure of the finance charge and the total of payments on a closed-end loan — Electronic Code of Federal Regulations, United States
• What is amortization? — the regulator's explanation of how a fixed payment splits between interest and principal, and why that split changes over the life of the loan — Consumer Financial Protection Bureau (United States)