Simple Loan Calculator

What this loan calculator does

You are borrowing a sum, at a rate, over a number of months, and you want to know the monthly payment before you sign anything.

This works it out. Enter the amount, the annual interest rate and the term in months, and it returns the monthly payment, the principal, and the total interest you will pay across the life of the loan.

That last figure is the one worth looking at hardest. The monthly payment is what determines whether you can afford the loan. The total interest is what determines whether the loan was a good idea.

The tool is called a simple loan calculator, and the word simple is doing something slightly misleading, which is worth clearing up before anything else.

Everything runs in your browser. Nothing typed here is stored or sent anywhere.

It is not a simple interest calculation

Simple here means straightforward rather than technical. What the tool actually computes is an amortised loan, which is the standard structure for mortgages, car finance and personal loans: equal monthly payments, interest charged on the balance remaining, and the balance falling to zero on the final payment.

That is a good thing, because it is what your lender is actually doing. But it is worth separating from simple interest in the technical sense, which is I = P × r × t and assumes the principal never moves.

The difference is large. On a 25,000 loan at 6 percent over five years:

Nearly double, and the amortised figure is the correct one. The reason is that you owe the full 25,000 only in month one. By the halfway point you owe roughly half of it, and you are charged interest on what you still owe rather than on what you originally borrowed.

Confusingly, lenders often describe exactly this kind of loan as a "simple interest loan", meaning only that interest is never charged on unpaid interest. That is true and it is not the same as the formula. Our simple interest calculator covers that distinction in more detail, and the short version is: if you are repaying in instalments, this page is the right one.

How to use it

1. Desired Loan Amount. The principal you are borrowing, after any deposit or trade-in.
2. Estimated Interest Rate. The annual rate as a percentage, so type 6.5 rather than 0.065. Use the APR if you have it, since it folds in most fees and is the fairer comparison figure.
3. Desired Loan Term. In months, not years. A thirty year mortgage is 360, a five year car loan is 60, and this is the field people most often fill in wrongly.

Press Calculate. Press Reset to clear it.

One limitation to note: the rate has to be above zero. Genuine zero percent finance exists, particularly on car promotions, and this tool will refuse it. The maths is easy in that case anyway, since with no interest the payment is simply the amount divided by the number of months. A 25,000 loan over 60 months at 0 percent is 416.67 a month. We are adding that case.

The formula

M = P × [ i(1 + i)ⁿ ] ÷ [ (1 + i)ⁿ − 1 ]

Where M is the monthly payment, P is the principal, i is the monthly interest rate, meaning the annual rate divided by 12 and by 100, and n is the number of monthly payments.

It looks worse than it is. What the formula does is find the payment at which the present value of all your future payments exactly equals the amount you borrowed. It is the annuity formula from the time value of money, rearranged to solve for the payment rather than the total, and it is the same arithmetic our sinking fund calculator uses in the other direction.

Then the two summary figures:

Total paid = monthly payment × number of payments

Total interest = total paid − principal

Notice what the formula assumes: a fixed rate for the whole term, every payment made on time, and no overpayments. Change any of those and the real total differs.

A worked example

A 300,000 mortgage at 6.5 percent over 360 months.

The monthly rate is 6.5 ÷ 100 ÷ 12 = 0.0054167. The number of payments is 360.

Monthly payment: 1,896.20

Total paid: 1,896.20 × 360 = 682,633

Total interest: 382,633

So over thirty years you repay the 300,000 you borrowed and hand over another 382,633 on top. The interest exceeds the loan.

Two smaller examples for contrast:

The third row is not worse because the rate is higher. It is worse because the term is thirty years, and time is what makes interest expensive.

Where each payment actually goes

Every payment splits into interest and principal, and the split changes dramatically over the life of the loan. Most people know this in the abstract and are still surprised by the numbers.

Taking that 300,000 mortgage at 6.5 percent, with a payment of 1,896.20:

In the first payment, 86 percent goes to interest and 271 comes off the balance. After a full year of payments totalling nearly 23,000, the balance has fallen by about 3,400.

It takes until roughly payment 240, twenty years in, before more of the payment goes to principal than interest. That is the crossover, and it sits much later than people expect.

Two practical consequences fall out of that shape.

Early overpayments are worth far more than late ones. An extra 271 paid alongside the first payment removes an entire month of principal, and every future interest charge is calculated on a smaller balance. The same 271 paid in year 25 does almost nothing by comparison. If you are going to overpay, do it early.

Selling early means you have built little equity. Five years into a thirty year mortgage you have paid nearly 114,000 and still owe about 280,000. That is worth knowing before assuming a few years of payments have bought you a substantial stake.

What the term does to the total

Stretching a loan over more months reduces the payment, which is why it gets offered. It also increases the total considerably, which is less often mentioned.

The relationship is not symmetric. Doubling the term does not double the interest, it does rather worse than that, because you are carrying a larger balance for longer at every point.

The rule of thumb worth taking away: the payment is what you can afford, the total is what it costs. A lender optimising for the first will happily let you ignore the second, and the difference between a five and a seven year car loan is usually a smaller monthly figure and a noticeably larger total.

The same logic runs the other way on overpayments. Because interest accrues on the balance, shortening the effective term by paying extra cuts the total by more than the extra payments themselves. On a long mortgage the effect is substantial, and it is worth checking whether your agreement allows overpayment without penalty, because some do not.

If you want to compare two offers properly, compare the total paid rather than the monthly figure, and make sure both are quoted as APR rather than a headline rate.

What the payment figure leaves out

The number this tool returns is principal and interest only. Several things ride alongside it in practice.

On a mortgage, the actual monthly outgoing usually includes property tax and homeowner's insurance collected through escrow, and often mortgage insurance if the deposit was small. Together these are quoted as PITI, and they can add a substantial amount. Our property tax calculator covers the tax component.

Fees. Arrangement fees, origination fees, valuation and legal costs. Some are payable up front and some get added to the loan, in which case you pay interest on them too. This is exactly why APR exists as a measure: it folds most fees into a single comparable rate, whereas a headline interest rate does not.

Variable rates. The formula assumes the rate holds for the whole term. On a variable or tracker product it will not, and the payment moves with it.

Early repayment charges. Some agreements penalise overpaying or settling early, which can undo the benefit described above. Worth checking before making a plan around it.

Insurance products sold alongside the loan, which may be optional even when they are not presented that way.

So treat the monthly payment here as the core of the cost rather than the whole of it, and ask any lender for a total amount payable rather than a monthly figure.

Questions people ask

How is a loan payment calculated?

With the amortisation formula: principal times the monthly rate times (1 plus the monthly rate) to the power of the number of payments, divided by that same power minus one. It finds the payment at which the loan reaches zero exactly on schedule.

Do I enter the term in years or months?

Months. Thirty years is 360, five years is 60. This is the most common input mistake here.

Is this simple interest?

No. It is an amortised loan, where interest is charged on the falling balance. Simple interest in the technical sense would overstate the cost by roughly double on a typical instalment loan.

Can I model a zero percent loan?

Not currently, the rate must be above zero. With no interest the payment is just the amount divided by the number of months.

Does paying extra actually help?

Considerably, and much more early than late. An extra payment in the first year removes principal that would otherwise have accrued interest for decades.

Should I use the interest rate or the APR?

The APR if you have it, since it includes most fees and is designed for comparing offers. The plain rate understates the true cost where fees are involved.

Why is my total interest more than the loan itself?

Long terms. On a thirty year mortgage at 6.5 percent the interest exceeds the principal, because you are borrowing a large sum for a very long time.

Is this my full monthly housing cost?

No, this is principal and interest. Property tax, insurance and any mortgage insurance are added on top, usually through escrow.

References

A note on sourcing. The amortisation formula is the standard annuity result from the time value of money, solved for the periodic payment. The annual percentage rate, which is the figure lenders must disclose and the fairer basis for comparing offers, is defined in the United States by the Truth in Lending Act and Regulation Z.

1. OpenStax, Principles of Finance, Section 8.2, Annuities. https://openstax.org/books/principles-finance/pages/8-2-annuities
2. OpenStax, Principles of Finance, Section 7.2, Time Value of Money Basics. https://openstax.org/books/principles-finance/pages/7-2-time-value-of-money-tvm-basics
3. Kellison, S. G., The Theory of Interest, 3rd edition, McGraw-Hill, 2008.
4. Bankrate, How to Calculate Loan Interest. https://www.bankrate.com/loans/personal-loans/how-to-calculate-loan-interest/