Work out a loan’s rate from its repayments, or convert a nominal, annual equivalent or monthly rate.
Nominal annual rate
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Enter the amount borrowed, any fee paid at the start, each repayment and how many repayments there are. The calculator finds the rate per period, the nominal annual rate and the annual equivalent rate, with every step shown. The second mode converts a nominal, annual equivalent or per-period rate into the other two.
Take the amount borrowed, the repayment and the number of repayments from your agreement or repayment schedule. With a repayment of interest and capital only, the result is the loan’s interest rate. To get close to the APR, add any compulsory charges to the repayment and enter any fee paid at the start, such as an arrangement fee: it is taken off the sum you receive.
The nominal annual rate is the rate per period times the number of periods in a year: 0.5% a month is 6% a year. The annual equivalent rate allows for interest on interest: (1 + rate per period) to the power of the periods in a year, minus 1, so 0.5% a month is 6.168% a year. An APR is an annual rate of this kind that equates the amount lent with every repayment and charge.
Amounts are exact to the penny. Rates are rounded to the nearest figure: four decimal places for the rate per period and three for the annual rates. The APR figure is also given to one decimal place, rounded up when the next figure is 5 or more, as the rules for the APR of consumer buy-to-let mortgages require (SI 2015/910, Schedule 2, paragraph 20). The calculator assumes equal repayments at the end of each period, and the arithmetic is the same in England, Scotland, Wales and Northern Ireland.
Rate per period i: the value for which amount borrowed = repayment × [1 − (1 + i)^−n] ÷ i, n being the number of repayments, found by successive approximation.
Nominal annual rate = i × periods in a year (12 for monthly repayments).
Annual equivalent rate = (1 + i)^12 − 1 for monthly repayments.
Converting: rate per period = nominal rate ÷ 12, or (1 + annual equivalent rate)^(1/12) − 1.
You repay £231.24 × 36 = £8,324.64, of which £824.64 is interest. The rate that balances the £7,500 lent against the 36 repayments is 0.5751% a month: a nominal annual rate of 6.901% (the unrounded monthly rate × 12) and an annual equivalent rate of 7.124%. If each repayment includes every charge, the APR is 7.1%.
There is no direct formula: the monthly rate is the value of i for which the amount borrowed equals the repayment × [1 − (1 + i)^−n] ÷ i, n being the number of repayments. The calculator finds it by successive approximation. You only need the amount borrowed, the monthly repayment and the number of repayments.
The nominal interest rate is the monthly rate times 12. The APR adds compulsory fees and charges and is an annual equivalent rate, so it allows for interest on interest. With no fees at all, a nominal rate of 5% repaid monthly already gives an APR of 5.1% (5.116% before rounding).
Because interest is added each period and then earns interest itself. 1% a month is 12% a year nominal but 12.683% as an annual equivalent rate, since 1.01 to the power of 12 is 1.12683 to five decimal places. With yearly repayments the two rates are the same.
There is no general cap on the rate of interest in a consumer credit agreement, as HMRC’s interest rate review notes. High-cost short-term credit, such as payday loans, is the exception: the FCA caps its cost under section 137C of the Financial Services and Markets Act 2000. The review describes the cap as 0.8% a day in interest and fees, with a total cost of no more than the amount borrowed; check the FCA’s current rules before relying on these figures.
The repayment in the agreement is rounded to the penny, which moves the recalculated rate by a few thousandths. A first repayment at a different date, a fee paid separately or a final repayment of a different amount also make a difference: the calculator assumes equal repayments at the end of each period.
This calculator gives general information, not legal, tax, financial or accounting advice. The rate of a loan is the one in its agreement: check it with the lender or an adviser.
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