Calculating Loan Interest
There are many types of loans: you can take out a mortgage, a consumer loan, a payday loan, or use a payment card's credit feature, where any unpaid balance becomes interest-bearing after the due date. Almost the same principles apply to all loan types.
Loans typically have a nonzero interest rate. The loan's interest rate refers to the nominal annual rate, stated as a percentage. For example, a 12% rate means 12% of the principal is added to the principal each year if interest is calculated once a year. Interest can also be calculated multiple times during the year.
Many variables affect the costs of loans taken through credit cards. For small loans, interest is typically calculated monthly. In that case, the nominal annual rate is divided by 12 to use it for monthly calculations. After each month, interest is calculated on the principal at the monthly rate and added to the principal.
When interest is calculated monthly, the compound interest effect occurs. Interest is calculated on the principal that already includes earlier interest charges. This leads to a situation where total interest costs are higher than the annual rate suggests. The lender may also charge a monthly account fee and possibly an opening fee with the first bill. In the end, the total cost of the loan is clearly higher than the nominal annual rate implies. The nominal rate does not tell the whole truth about a loan's costs.
Annual Interest Rate
Annual interest rate usually refers to the nominal rate shown in the loan details. It shows how much interest is added to the principal if interest is calculated once a year. However, interest may be calculated more frequently, so calculating the annual percentage rate provides a clearer picture of the loan's cost.
Annual Percentage Rate
Regulators require that loans have an annual percentage rate. This is a theoretical percentage calculated by accounting for all loan costs on the principal. The annual percentage rate includes compound interest, opening fees, and the monthly administration fee. Therefore, the annual percentage rate is almost always significantly higher than the nominal rate. The benefit of the annual percentage rate is that it makes it easy to compare loan costs.
Compound Interest Formula
There is an exact formula for determining the annual percentage rate:
On the left side of the formula is the total loan amount if the loan was drawn in one lump sum. On the right side is the sum of all repayments. D's indicate the size of each repayment, and S's the time between the loan disbursement and the repayment, expressed as fractions of a year.
Questions and Answers
- How is a loan's interest calculated?
- It is best to calculate the annual percentage rate for a loan. The annual percentage rate is a comparison value for the loan that includes its interest and other fees. The annual percentage rate takes all costs into account and shows what rate would correspond to a loan of the same size if the only cost were interest calculated annually.
- How is the annual percentage rate calculated?
- The annual percentage rate is a bit difficult to calculate by hand, even with a basic calculator, because it involves a summation formula. The easiest way is to use a calculator, which you can also find on our site.
- What is a good interest rate for a credit card?
- An annual percentage rate under 10 per cent is excellent for a credit card.
Annual Percentage Rate Calculator
Below, we offer a calculator for determining the annual percentage rate. This calculator is intended primarily for calculating the APR of a credit card loan, but it can also be used to calculate the APR of other loans, such as a mortgage. The calculator makes the following assumptions:
- The loan is drawn in full at once.
- Repayments are equal in size, but the opening fee is paid with the first monthly payment.
- Interest is calculated monthly.