Loan Repayment Calculator UK: Monthly Payments and Total Interest

How the calculation works

The monthly payment is calculated using the formula monthly payment = P x r / (1 - (1 + r)^-n). In this formula, P is the amount borrowed, r is the APR divided by 12 expressed as a decimal, and n is the number of months in the term. The calculator treats the APR as a nominal annual rate compounded monthly, which is an approximation. This method produces a fixed monthly instalment that covers both interest and capital over the agreed term. The result depends on the amount borrowed, the APR and the term length. The same formula applies to different inputs, so a change in any one input changes the monthly payment.

A worked example shows how the inputs affect the result. A loan of £10,000 at 6.9% APR over 5 years costs £197.54 a month, £11,852.43 in total and £1,852.43 in interest. The total cost is the monthly payment multiplied by the number of months, and the interest is the total cost minus the original £10,000. The example uses the same formula and the same treatment of APR as a nominal annual rate compounded monthly. Changing the APR, the amount borrowed or the term changes the monthly payment and the total interest. The figures in the example are specific to the stated inputs, so a different set of inputs produces different figures.

APR vs representative APR

Representative APR is a rate used in promotions. The two rates serve different purposes. Under FCA CONC 3.5, at least 51% of borrowers accepted from a promotion must get that rate or lower. The representative APR is therefore not necessarily the rate every borrower receives. A lender may offer a different personal APR after a credit check. The personal APR reflects the individual circumstances of the borrower. The representative APR gives a benchmark for the promotion, while the personal APR gives the rate offered to a particular borrower after the credit check. The requirement means that a promotion cannot advertise a representative APR that fewer than 51% of accepted borrowers receive.

The difference matters because the monthly payment and total cost depend on the APR used. In the worked example, £10,000 at 6.9% APR over 5 years costs £197.54 a month, £11,852.43 in total and £1,852.43 in interest. If the personal APR differs from the representative APR, the monthly payment and total interest will differ from that example. The representative APR is the rate that at least 51% of accepted borrowers from the promotion must receive or beat. The personal APR is the rate offered after a credit check. The formula monthly payment = P x r / (1 - (1 + r)^-n) uses the APR as r, so a different APR changes the result.

Term length trade-off

A longer term lowers the monthly payment but raises total interest. This relationship follows from the formula. The formula monthly payment = P x r / (1 - (1 + r)^-n) shows that n is the number of months. Increasing n spreads the capital and interest over more months, so each monthly payment is smaller. The total interest rises because interest is charged for a longer period. A shorter term has the opposite effect: the monthly payment is higher and the total interest is lower. The trade-off is between the size of the monthly payment and the total interest paid over the term. The worked example uses a 5 year term.

In the worked example, £10,000 at 6.9% APR over 5 years costs £197.54 a month, £11,852.43 in total and £1,852.43 in interest. A different term changes these figures. A longer term would lower the £197.54 monthly payment but would raise the total interest above £1,852.43. A shorter term would raise the monthly payment but would lower the total interest below £1,852.43. The exact figures depend on the term and the APR. The calculator treats APR as a nominal annual rate compounded monthly, an approximation. The relationship between term length and total interest follows from n in the formula monthly payment = P x r / (1 - (1 + r)^-n).

Repaying early and withdrawal

Borrowers can repay early. Lenders can charge a limited early settlement fee under the Consumer Credit (Early Settlement) Regulations 2004, up to about 58 days' interest. Early settlement reduces the remaining interest because the loan is paid off sooner. The fee is limited by those regulations. The amount of interest saved and the fee charged depend on the terms of the agreement and the timing of the repayment. Consumer credit agreements usually give a 14-day right to withdraw under the Consumer Credit Act 1974 s66A. The right to withdraw and early settlement are separate rights. The fee limit applies to the early settlement charge. The right to withdraw is a separate statutory right.

The 14-day right to withdraw under the Consumer Credit Act 1974 s66A allows a borrower to withdraw from a consumer credit agreement within that period. Early settlement under the Consumer Credit (Early Settlement) Regulations 2004 allows a borrower to repay early, and the lender can charge a limited fee of up to about 58 days' interest. The worked example of £10,000 at 6.9% APR over 5 years costs £197.54 a month, £11,852.43 in total and £1,852.43 in interest. Repaying early changes the total interest from that example because the loan is not held for the full 5 years. The fee limit and the right to withdraw are separate rules. The formula uses the term in months, so early repayment shortens the period over which interest is charged.

Frequently asked questions

How is the monthly payment calculated?

The monthly payment uses the formula monthly payment = P x r / (1 - (1 + r)^-n). P is the amount borrowed, r is the APR divided by 12 as a decimal, and n is the number of months. The calculator treats APR as a nominal annual rate compounded monthly, an approximation. For £10,000 at 6.9% APR over 5 years, the payment is £197.54.

What is a representative APR?

Representative APR is a rate used in promotions. Under FCA CONC 3.5, at least 51% of borrowers accepted from a promotion must get that rate or lower. The representative APR is not necessarily the rate every borrower receives. A lender may offer a different personal APR after a credit check. The personal APR reflects the individual circumstances of the borrower.

Does a longer term reduce total interest?

A longer term lowers the monthly payment but raises total interest. The formula monthly payment = P x r / (1 - (1 + r)^-n) shows that n is the number of months. Increasing n spreads the capital and interest over more months, so each payment is smaller. The total interest rises because interest is charged for a longer period.

Can a borrower repay early?

Borrowers can repay early. Lenders can charge a limited early settlement fee under the Consumer Credit (Early Settlement) Regulations 2004, up to about 58 days' interest. Early settlement reduces the remaining interest because the loan is paid off sooner. The fee is limited by those regulations. The amount of interest saved and the fee charged depend on the terms of the agreement and the timing of the repayment.

Is there a right to withdraw?

Consumer credit agreements usually give a 14-day right to withdraw under the Consumer Credit Act 1974 s66A. The right applies within that period. The right to withdraw and early settlement are separate rights. Early settlement allows a borrower to repay early, and the lender can charge a limited fee of up to about 58 days' interest.