Loan Calculator

A = P × r × (1 + r)^n ÷ ((1 + r)^n − 1), and total interest = A × n − P after the last payment is balanced

P

The amount borrowed — the principal

r

Monthly interest rate: the annual rate divided by twelve

n

Number of payments: the loan term counted in months

A

The level monthly payment, rounded to the cent

ΣI

Total interest over the whole loan: every month's interest added up

Use it to turn three numbers you already know into the one you are shopping for, and then to see what moving each of them does. The rate is the number most people have least control over — it comes from the lender and the market rather than from you — while the term is the one that is usually yours to choose, and it moves the total interest far more than it moves the payment. Halving a thirty year term does not halve the monthly payment; it raises it by about a third and cuts the interest roughly in half. Run the numbers both ways before deciding whether the lower payment is worth the extra interest, and check what the payment would be if the rate came back a point higher.

1. A 250,000 loan at 6.5% over thirty years

   1. Monthly rate: 6.5 ÷ 12 = 0.541667% a month, which is 0.00541667 as a decimal
   2. Payment: 250,000 × 0.00541667 × 1.00541667^360 ÷ (1.00541667^360 − 1) = 1,580.17
   3. Total paid: 1,580.17 a month for 360 months, with the last payment trimmed to 1,580.55 to land the balance exactly on zero, gives 568,861.58
   4. Total interest: 568,861.58 − 250,000 = 318,861.58
   5. Interest share: 318,861.58 ÷ 568,861.58 = 56.1%

   This is the page's default. The first payment is 1,354.17 of interest and only 226.00 of principal, and the loan is more than half repaid by the time the split is even — which is the whole reason a thirty year term costs so much more than a fifteen year one.

2. A 10,000 loan at 7.5% over five years

   1. Monthly rate: 7.5 ÷ 12 = 0.625% a month, which is 0.00625 as a decimal
   2. Payment: 10,000 × 0.00625 × 1.00625^60 ÷ (1.00625^60 − 1) = 200.38
   3. Total paid: sixty payments, the last one 200.35 rather than 200.38, giving 12,022.77
   4. Total interest: 12,022.77 − 10,000 = 2,022.77
   5. Interest share: 2,022.77 ÷ 12,022.77 = 16.8%

   Same formula, very different shape: a short term on a small amount keeps the interest share under a fifth, against 56.1% on the thirty year loan above. Length of term, not the rate, is what separates these two numbers.

3. A 10,000 loan at 0% over two years

   1. Zero rate: the formula divides by (1 + 0)^n − 1, which is zero, so it cannot be used at all
   2. Payment: 10,000 ÷ 24 = 416.67
   3. Total interest: nothing accrues at 0%, so 0
   4. Total paid: 10,000 — the loan is exactly the sum of its payments once the last one is trimmed to 416.59
   5. Interest share: 0 ÷ 10,000 = 0%

   Zero-rate finance is a real product, not a theoretical corner, and it is the one case where the formula breaks down rather than merely getting slow — so it is handled separately. Every payment is principal, which is why the interest share is exactly zero rather than a very small number.

The arithmetic is exact and the inputs are yours; what the page cannot see is the rest of the loan. Rates on most loans are variable after an initial fixed period, and this page assumes the rate you enter holds for the whole term — for an adjustable-rate loan, run it again at the rate you would face after the reset and treat the two answers as the range you are choosing between. Fees are not in here: origination charges, arrangement fees and any insurance the lender requires are added to what you pay without ever appearing in an interest figure, and on a small short loan they can matter more than the rate. Nothing here models early repayment, overpayment or a lump sum, all of which shorten the term and cut the interest, and the balance does not move with inflation — 250,000 repaid over thirty years is not 250,000 in today's money. The amounts carry no currency symbol, so they are right in whatever currency you typed them in and meaningless in any other. Finally, the schedule is monthly and the interest compounds monthly; a loan that charges interest daily, or one with a payment holiday at the start, will not match this to the cent.

How is the monthly payment on a loan worked out?

With the amortisation formula: the amount borrowed times the monthly interest rate times (1 + rate) to the power of the number of months, divided by (1 + rate) to that same power minus one. The rate is the annual rate divided by twelve, and the answer is rounded to the cent. Every month you pay that same amount, but the split inside it changes — the interest is charged on whatever balance is left, so the interest falls and the principal rises month by month.

Why is the total interest so much larger than the amount I borrowed?

Because the term is long and interest is charged on the balance every month. At 6.5% over thirty years, 250,000 costs 318,861.58 in interest — more than the loan itself. The rate is only part of it: the same loan over fifteen years pays roughly a third of that interest at a slightly higher monthly payment. Time is what multiplies the interest, which is why the term field is the one to experiment with.

What counts as a fixed rate loan?

One where the interest rate stays the same for the whole term, so the monthly payment never changes. Most car loans and personal loans are fixed; many mortgages are fixed only for an initial period and then move with the market. This page assumes the rate you enter holds throughout, so for a loan with a reset, work out the payment at the rate you would face after it.

Should I choose a longer term to keep the monthly payment down?

That is the trade the term field exists to show you. Stretching a loan out lowers the payment and raises the total interest, and the two do not move at the same rate: going from fifteen to thirty years cuts the payment by roughly a third and roughly doubles the interest. If the lower payment is the only way to afford the loan, take it and overpay later; if you can carry the higher payment, the interest saved is real money.

Does this loan calculator include fees and insurance?

No. It prices the loan itself: principal, interest rate and term. Origination fees, arrangement fees, late charges and any insurance the lender insists on are separate costs that do not show up as interest, and on a small or short loan they can outweigh the rate difference between two offers. Ask for the total amount payable — the figure that includes every charge — and compare that rather than the payment alone.

Why does the last payment differ from all the others?

Because each month's interest is rounded to the cent, and the rounded amounts do not add up to the balance exactly. On 250,000 at 6.5% over thirty years, 359 payments of 1,580.17 leave eight cents behind, so the final payment is 1,580.55 and the balance lands on zero. Lenders do the same thing — the loan is finished when the balance is zero, not when the last scheduled payment is made.

• H.15 Selected Interest Rates — the daily rates this page's annual rate field stands in for — Board of Governors of the Federal Reserve System (United States)
• Compound Interest Calculator — how a balance grows when interest is charged on it every period — U.S. Securities and Exchange Commission (Investor.gov)