How is a loan payment calculated?
An installment loan with a fixed rate has one level payment, set so that the last payment leaves nothing owed. The formula is PMT = L x i / (1 - (1 + i)^-n), where L is the amount borrowed, i the interest rate per payment period and n the number of payments. Each period's rate is the annual rate over the count of payments in a year: 12 for monthly, 26 for every two weeks and 52 for weekly.
With the defaults, $25,000 at 7.5% over 5 years paid monthly has i = 0.075 / 12 = 0.625% and n = 60. The payment is $500.95 a month. Sixty payments total $30,056.92, so the interest is $5,056.92. Each payment first covers the interest on the balance still owed, and the rest reduces the loan: in year 1, $1,729.81 of the $6,011.38 paid is interest, and the balance falls to $20,718.42.
How much can I borrow for the payment I can afford?
Turn the formula round and it gives the loan a payment will support: L = PMT x (1 - (1 + i)^-n) / i. This is the present value of the payments at the loan's rate. Choose the Amount tab, enter the payment, the rate and the years, and the headline is the most that payment repays.
At 7.5% over 5 years, $550 a month repays $27,447.92. The answer moves with each input: a lower rate or a longer term lets the same payment carry a larger loan, and a higher rate shrinks it. The figure is arithmetic only. A lender also looks at income, other debts and credit history, and none of those are in this calculation.
How long will it take to pay off a loan?
The Term tab solves for the number of payments: n = -ln(1 - L x i / PMT) / ln(1 + i). The answer is rarely a whole number, so the calculator rounds it up and makes the final payment smaller, just enough to clear what is left.
Paying $550 a month on $25,000 at 7.5% gives n = 53.64, so the loan takes 54 payments, or 4 years 6 months. The first 53 payments are $550 and the last is $351.99. Total interest is $4,501.99, which is $554.93 less than the 5-year loan above, because the balance falls faster. At $300 a month the same loan takes 119 payments, 9 years 11 months, and costs $10,424.24 of interest.
There is a floor. In the first month the loan charges $25,000 x 0.625% = $156.25 of interest. A payment of $156.25 or less never reduces the balance, and the calculator says so instead of returning a term.
What interest rate is a loan really charging?
When you know what you borrowed, what you pay and for how long, the Rate tab finds the interest rate those figures imply. There is no formula that isolates the rate, so the calculator searches for the rate per period at which the payments are worth exactly the loan today, then multiplies it by the payments a year.
Borrowing $25,000 and paying $550 a month for 5 years implies 0.9596% a month, or 11.51% a year. Compounded monthly, that is an effective annual rate of 12.14%. If the payments add up to exactly the amount borrowed, the rate is 0%; if they add up to less, no positive rate fits and the page says so.
This is the rate on the money you actually received. If a fee was taken from the loan before it reached you, enter the amount you received, not the amount on the agreement, and the result moves toward an APR. The APR calculator works through fees, and the US and UK ways of stating an APR, in full.
Monthly, biweekly or weekly payments: what difference does it make?
At the same annual rate, more frequent payments reduce the balance a little sooner, so a little less interest builds up. On the default loan of $25,000 at 7.5% over 5 years:
| Payments | Each payment | Number | Paid in a year | Total interest | Effective annual rate |
|---|---|---|---|---|---|
| Monthly | $500.95 | 60 | $6,011.38 | $5,056.92 | 7.763% |
| Every two weeks | $230.89 | 130 | $6,003.08 | $5,015.41 | 7.777% |
| Weekly | $115.38 | 260 | $5,999.52 | $4,997.60 | 7.783% |
Weekly payments save $59.32 of interest over the five years, and every two weeks saves $41.51. The effective annual rate rises slightly with frequency, because interest is charged more often, yet total interest still falls, because the balance shrinks between charges.
A much larger saving comes from paying half the monthly amount every two weeks, which is not the same thing. Half of $500.95 is $250.47, and 26 of those a year come to $6,512.33, the same as 13 monthly payments. On this loan that clears the debt in 118 payments, about 4 years 28 weeks, with $4,526.77 of interest, $530.15 less than paying monthly. The saving comes from paying more each year, not from the timing.
Worked examples in pounds and dirhams
The arithmetic does not change with the currency, and no amount is ever converted. These rates are chosen to illustrate the method, not taken from any lender.
| Loan | Rate and term | Payments | Each payment | Total interest |
|---|---|---|---|---|
| £15,000 | 6.9%, 4 years | Monthly | £358.50 | £2,207.91 |
| £15,000 | 6.9%, 4 years | Every two weeks | £165.24 | £2,184.87 |
| AED 80,000 | 6%, 3 years | Monthly | AED 2,433.76 | AED 7,615.18 |
| AED 80,000 | 6%, 3 years | Weekly | AED 560.65 | AED 7,461.90 |
The pound loan saves £23.04 by switching to two-weekly payments, and the dirham loan AED 153.28 by switching to weekly ones. Pick GBP or AED in the currency selector and the symbols and decimals follow; untouched defaults resize to round amounts for that currency.
How do the rate and the term change a loan?
On $25,000 over 5 years, each two points on the rate adds about $23 to $25 a month:
| Rate | Monthly payment | Total interest |
|---|---|---|
| 5.5% | $477.53 | $3,651.74 |
| 7.5% | $500.95 | $5,056.92 |
| 9.5% | $525.05 | $6,502.79 |
| 11.5% | $549.82 | $7,988.91 |
The term pulls the other way. At 7.5%, the same loan costs $777.66 a month over 3 years, $500.95 over 5, $383.46 over 7 and $296.75 over 10, while total interest climbs from $2,995.60 to $10,610.53. Stretching from 3 to 10 years cuts the payment by more than 60% and adds $7,614.93 of interest. At 0% the payment is simply the loan divided by the number of payments: $416.67 a month over 5 years.
How do you calculate a loan in Excel?
Excel has one function for each tab of this calculator. Microsoft's documentation gives the syntax as PMT(rate, nper, pv, [fv], [type]), PV(rate, nper, pmt, [fv], [type]), NPER(rate, pmt, pv, [fv], [type]) and RATE(nper, pmt, pv, [fv], [type], [guess]). Keep the units consistent: a monthly loan uses the annual rate divided by 12 and the number of months.
- Payment: =PMT(7.5%/12, 60, -25000) returns 500.95.
- Amount: =PV(7.5%/12, 60, -550) returns 27,447.92.
- Term: =NPER(7.5%/12, -550, 25000) returns 53.64 payments, which this calculator rounds up to 54.
- Rate: =RATE(60, -550, 25000)*12 returns 11.51%.
The money you receive and the money you pay need opposite signs, which is why the payment or the loan is entered as negative. Microsoft notes that RATE is found by iteration and returns the #NUM! error if it does not settle; its own example, a 4-year loan of 8,000 repaid at 200 a month, gives an annual rate of 9.24%. For biweekly payments, divide by 26 and count the payments in two-week steps.
Common mistakes and what this calculator leaves out
- Comparing payments across frequencies. $115.38 a week is not cheaper than $500.95 a month; it is the same loan paid in smaller steps.
- Reading an implied rate as an APR. The rate tab treats the loan amount as the money you received. Fees taken at the start change the answer.
- Treating the borrowable amount as an approval. It is what a payment can repay at a rate you enter, nothing more.
- Forgetting the short final payment. A term that is not a whole number of payments ends with a smaller one.
The calculator assumes a fixed rate, level payments at the end of each period, interest charged each period at the annual rate divided by the payments a year, and the first payment one period after the loan starts. It leaves out fees, insurance, taxes, late charges and early repayment charges, rate changes on variable loans, and the exact day counts some lenders use. For a home loan with overpayments, see the mortgage calculator.
Glossary
Principal: the amount borrowed, and the part of each payment that reduces it. Installment loan: a loan repaid in equal payments over a set term. Rate per period: the annual rate divided by the number of payments a year. Effective annual rate: what a year of compounding at the rate per period amounts to, (1 + i)^k - 1. Term: the time over which the loan is repaid. Biweekly: every two weeks, 26 payments a year, also called fortnightly. Balance: what is still owed after a payment. Present value: what a stream of future payments is worth today at a given rate.
Frequently asked questions
What is the monthly payment on a $25,000 loan?
At 7.5% over 5 years it is $500.95 a month, with $5,056.92 of interest in total. Over 3 years at the same rate it is $777.66 a month and $2,995.60 of interest.
How do I calculate how much I can borrow?
Multiply the payment by (1 - (1 + i)^-n) / i, where i is the rate per payment and n the number of payments. At 7.5% over 5 years, $550 a month repays $27,447.92. A lender's own limit also depends on income and other debts.
How long will it take to pay off my loan?
Use n = -ln(1 - L x i / PMT) / ln(1 + i) and round up. A $25,000 loan at 7.5% paid at $550 a month takes 54 payments, 4 years 6 months, with a final payment of $351.99.
How do I find the interest rate on a loan?
Search for the rate per period at which the payments are worth the loan today, then multiply by the payments a year. Borrowing $25,000 and paying $550 a month for 5 years implies 11.51% a year. In Excel, =RATE(60, -550, 25000)*12 gives the same answer.
Do weekly payments save interest?
A little, at the same annual rate. On $25,000 at 7.5% over 5 years, weekly payments of $115.38 cost $4,997.60 of interest against $5,056.92 paid monthly, a saving of $59.32.
Is paying every two weeks the same as paying monthly?
Not if you pay half the monthly amount every two weeks. That makes 26 half payments a year, the same as 13 monthly ones, and on the default loan it saves $530.15 of interest. Paying the exact two-weekly equivalent saves only $41.51.
What happens if my payment is too small?
If the payment is no more than the interest charged each period, the balance never falls. On $25,000 at 7.5%, the first month's interest is $156.25, so a monthly payment must be higher than that to repay anything.
Can I use this loan calculator in pounds or dirhams?
Yes. Choose GBP, AED or another of the 24 currencies and amounts are shown in that currency, never converted. £15,000 at 6.9% over 4 years costs £358.50 a month.
Is the rate in this calculator an APR?
It is the annual interest rate charged on the balance. An APR also counts certain fees, and the US and UK express it differently. Without any fees, a US APR equals this rate, while the UK figure is the effective annual rate.
What is the effective annual rate on a 7.5% loan?
It depends on how often interest is charged. Monthly, (1 + 0.075 / 12)^12 - 1 = 7.763%. Every two weeks it is 7.777%, and weekly 7.783%.
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Last reviewed 14 November 2026 by the NIFM Academy editorial team. Next review by 14 November 2027.
- Loan annuity formulas, standard fixed-rate arithmetic for the payment, the present value, the number of payments and the rate by iteration, reproduced in the working under every result. Checked 14 November 2026.
- Microsoft Support, PMT, PV, NPER and RATE functions, syntax of each function; RATE is calculated by iteration and returns #NUM! if it does not converge; the RATE example of a 4-year 8,000 loan at 200 a month giving 9.24% a year; keep units consistent for monthly payments. Checked 14 November 2026.