Personal loan calculator

How is a personal loan payment calculated?

Most personal loans charge interest on the balance still owed, each month, at the annual rate divided by 12, and are repaid in equal monthly payments. The payment is L x i / (1 - (1 + i)^-n), with L the loan, i the monthly rate and n the number of months. For the default $10,000 at 9.9% over 36 months, i = 0.825% and the payment is $322.20. The 36 payments total $11,599.29, of which $1,599.29 is interest.

That is the cost before any fee. What makes a personal loan calculator different from a plain loan calculator is the fee, and the APR it produces. A fee changes either what you receive or what you owe, while the payments run on as before, so the true cost of the money is higher than the rate on the agreement.

How does an origination or arrangement fee change the APR?

The true APR is found from the money that actually changes hands: the cash you receive at the start and the payments you make. The calculator searches for the monthly rate at which the payments are worth exactly the cash you received, then states it as an annual rate.

Fee taken from the proceeds. A 5% fee on $10,000 means $9,500 reaches your account, but you still repay $10,000 plus interest: $322.20 a month. The monthly rate that discounts 36 payments of $322.20 to $9,500 is 1.1217%, which makes the true APR 13.46% by the US method and 14.32% by the UK method, against the 9.9% rate on the agreement. The total cost of borrowing is $11,599.29 - $9,500 = $2,099.29.

Fee added to the loan. If the $500 fee is added instead, you receive the full $10,000 and repay $10,500 with interest: $338.31 a month and $12,179.26 in total. The true APR is 13.28% (US) or 14.12% (UK). The cost of borrowing rises to $2,179.26, $79.97 more than the deducted fee, because interest is charged on the fee itself. The APR comes out lower only because more cash is in your hands.

Why does a fee raise the APR more on a short loan?

A fixed fee is spread over the months of the loan. Over a short term it is a large share of the cost of each month's borrowing; over a long one it thins out. With the same $10,000, 9.9% rate and 5% fee taken from the proceeds:

The APR falls as the term lengthens, yet the money paid for the loan rises: the 84-month loan costs $3,357.30 more than the 12-month one. A lower APR on a longer loan does not mean a cheaper loan. Compare APRs between loans of the same length, and compare total cost when the lengths differ. The chart beside the result draws this curve for your own fee.

Flat rate or reducing balance: how far apart are they?

A flat rate charges interest on the full amount borrowed for the whole term, even though you repay part of it every month. The interest is the loan x the rate x the years, added at the start and divided equally across the payments.

At 9.9% flat, $10,000 over 3 years carries $2,970 of interest, so each payment is $12,970 / 36 = $360.28, against $322.20 on a reducing balance. The true APR of that flat-rate loan, with no fee at all, is 17.75% by the US method and 19.27% by the UK method. Add the 5% fee taken from the proceeds and it reaches 21.48% and 23.73%. The flat-rate loan costs $1,370.71 more interest than the reducing one at the same quoted rate.

A dirham example: AED 50,000 at 5% flat over 48 months is AED 10,000 of interest and AED 1,250 a month. With a 1% processing fee taken from the proceeds you receive AED 49,500, and the true APR is 9.77% (US) or 10.22% (UK). Without the fee it is 9.24% or 9.64%. Choose On the full loan for the whole term to convert any flat rate.

Why are there two APRs: the US method and the UK method?

Both start from the same monthly rate, the one that makes the payments worth the cash received. They differ in how they turn it into a yearly figure.

• US method. Regulation Z, 12 CFR 1026.22 and its Appendix J, works the APR by the actuarial method and makes it the rate per unit-period multiplied by the number of unit-periods in a year: 12 for monthly payments. On the default loan that is 1.1217% x 12 = 13.46%.
• UK method. The FCA's consumer credit rules, CONC App 1.2.6R, define the APR through an equation that sets the present value of drawdowns equal to the present value of repayments and charges, on an annual basis. For equal monthly payments that is an effective annual rate: (1.011217)^12 - 1 = 14.32%. The rules require at least one decimal place, rounded half up, so a UK agreement could show it as 14.3%. EU lenders state an APRC worked out by the same annual equation, from Annex I of Directive 2008/48/EC, which is why euro amounts open on this method.

The UK figure is always the higher of the two once the rate is above zero, because it compounds the monthly rate. Even with no fee, 9.9% charged monthly shows as a 10.36% APR the UK way. When comparing offers, compare APRs worked out by the same method.

Worked examples in pounds

£7,500 over 48 months at a 6.4% interest rate, with a £150 arrangement fee added to the loan:

1. Loan: £7,500 + £150 = £7,650, while you receive £7,500.
2. Payment: £7,650 at 6.4% / 12 over 48 months is £181.07 a month, £8,691.20 in total.
3. Monthly rate on the cash received: the rate at which 48 payments of £181.07 are worth £7,500 is 0.6184%.
4. APR: (1.006184)^12 - 1 = 7.68% the UK way, which an agreement could show as 7.7%; 7.42% the US way.

Without the fee the payment would be £177.52 and the APR 6.59%. The £150 fee costs £170.42 over the term, because interest is charged on it for four years. Pick GBP in the currency selector and the headline switches to the UK method; any other currency starts on the US method, and either can be chosen.

How do you work out a personal loan APR in Excel?

Excel's RATE function returns the rate per period for a loan with level payments, found by iteration. Give it the number of payments, the payment as a negative number and the cash you received:

• US method: =RATE(36, -322.20, 9500)*12 returns 13.46%.
• UK method: =(1+RATE(36, -322.20, 9500))^12-1 returns 14.32%.

The key step is the third argument. Enter the money that reached you, $9,500, not the $10,000 on the agreement; using $10,000 just returns the 9.9% rate you started from. For a fee added to the loan, the payment is worked out on the larger loan with =PMT(9.9%/12, 36, -10500), and RATE then uses the $10,000 received. This calculator does the same thing in its working, with your own numbers.

Common mistakes and what this calculator leaves out

• Comparing a quoted rate with an APR. A 9.9% rate and a 13.46% APR can describe the same loan.
• Reading a flat rate as an APR. At 9.9% flat over 3 years, the true rate is about 1.8 times the flat figure.
• Choosing a longer term for its lower APR. The fee is spread thinner, but the total cost of borrowing grows.
• Calling a 0% loan with a fee free. A 5% fee taken from a 0% loan over 36 months is a true APR of 3.36% the US way.

The calculator assumes one fee paid at the start, equal monthly payments at the end of each month, the first payment one month after the money arrives, and a fixed rate. It does not include late fees, payment protection insurance, early repayment charges, odd first periods, or the exact day counts a lender may use. Which charges count in a disclosed APR is set by each country's rules; in the US, Regulation Z lists points and loan fees among finance charges. The lender's own disclosed APR is the figure to rely on. For a loan with no fee, the loan calculator also solves for the term or the rate.

Glossary

Origination fee: the US name for a charge to set up a loan, often a percentage of the amount. Arrangement fee: the UK name for the same kind of charge. Proceeds: the cash paid to you when the loan starts. APR: annual percentage rate, the cost of credit as a yearly rate, including fees as each country's rules require. Flat rate: interest charged on the original loan for the whole term. Reducing balance: interest charged only on what is still owed. Total cost of borrowing: everything repaid minus the cash received. Finance charge: in Regulation Z, the cost of consumer credit as a dollar amount.

Frequently asked questions

Courses at NIFM Academy

Sources and review