It can sometimes be challenging to compare and contrast interest rates charged on personal loans, credit cards, and other financial products. Thankfully, finance companies are now obliged to highlight nominal interest rates and the annual percentage rate (APR) due to regulatory obligations. So what does this mean, and where do periodic interest rates come in?
Nominal interest rate, APR and periodic interest rate
Before we delve deeper into the calculation of periodic interest rates, it is crucial to appreciate the nominal rate and APR.
Nominal interest rate
This is the rate of interest applied to your loan before any additional charges. The APR has superseded the nominal rate to give consumers a greater understanding of the actual cost of finance.
Example:
One-year loan of £10,000 at a nominal rate of 10% = annual interest of £1000
Repayment after one year: £11,000
APR
The APR is more reflective of the actual cost of loans and mortgages, taking interest charges and fees into account.
Example:
£200,000 loan at a nominal interest rate of 6% = £12,000 a year in interest
£200,000 loan + £5000 setup fee, at a nominal interest rate of 6% = £12,300 a year in interest
We know the nominal interest rate is 6%, but how does the setup fee impact the APR:
APR = 100 x (£12,300/£200,000) = 6.15%
For reference, if there was no setup fee in this example, the nominal rate would be the same as the APR.
Periodic interest rate
When calculating the periodic rate, it is essential to note that the APR figure does not include any element of interest on interest.
Example:
Let’s assume that you have a £10,000 loan with an APR of 12% with interest charged monthly. You would expect to pay £1200 a year in interest at face value. However, as interest is charged monthly, this is not the case with interest on interest.
To calculate the periodic rate, we first need to calculate the periodic rate. This is the APR divided by the number of compounding periods. So if interest is charged monthly, with a 12% APR, the periodic rate would be 1%. If the interest were charged quarterly, i.e. 4 compound interest rate periods, the periodic rate would be 3%.
Next, we need to calculate the impact of compound interest:
Interest charged monthly
To calculate the monthly periodic rate, you would multiply 1% to the power of 12 (the number of compound interest rate periods) = 12.68% periodic interest rate.
To highlight the impact of compound interest on higher rates, if the APR were 24%, the periodic interest rate would be 26.82%
Interest charged quarterly
To calculate the quarterly periodic rate, we simply multiply 3% to the power of 4 (the number of compound interest rate periods) = 12.55% periodic interest rate.
If the APR were 24%, the periodic interest rate would be 26.24%
The power of compound interest
Many people will look at these figures and see only minimal increases, even when considering monthly or quarterly interest periods. However, when you consider mortgage loans will often be in the hundreds of thousands of pounds over 20 years or more, the impact in extra interest charges can be significant. In addition, some mortgage companies will charge interest daily, increasing the periodic interest rate even further. So be wary of the small print!