The simple interest formula
Simple interest is paid only on the amount you start with, so it grows by the same amount every year. The formula is I = P × r × t, where P is the principal (the starting amount), r is the yearly rate as a decimal (5% is 0.05) and t is the time in years. The total is A = P + I.
For 10,000 at 5% for 3 years, I = 10,000 × 0.05 × 3 = 1,500, and the total is 11,500. The interest is 500 every year.
When the time is not in years, convert it first. Months are divided by 12, weeks by 52 and days by 365. Six months is 0.5 years, so 10,000 at 5% earns 250.
Finding the principal, the rate or the time
Rearrange the same formula to find whichever number is missing:
- Principal: P = I ÷ (r × t). To earn 1,500 at 5% in 3 years you need 1,500 ÷ (0.05 × 3) = 10,000.
- Rate: r = I ÷ (P × t) × 100. Earning 1,500 on 10,000 over 3 years is 5% a year.
- Time: t = I ÷ (P × r). Earning 1,250 on 10,000 at 5% takes 2.5 years, which is 2 years and 6 months.
When the time is not a whole number of months, the calculator gives it in days as well.
Simple interest against compound interest
With compound interest, each year's interest is added to the balance and earns interest too. Over 3 years, 10,000 at 5% reaches 11,576.25 with interest added once a year, against 11,500 with simple interest. The gap grows with time: after 20 years it is 26,532.98 against 20,000.
Simple interest suits short periods, or an interest rate that is fixed on a set amount. When interest is added to the balance, use the compound interest calculator. When you repay a loan in instalments, the balance falls as you pay, so a plain simple interest sum does not fit; the loan calculator works out each payment.
Days in a year
For a period in days, the interest depends on how many days the year is taken to have. Most calculations use 365. Some lenders use a 360 day year, which gives a little more interest for the same days. 90 days at 6% on 10,000 is 147.95 with 365 days and 150.00 with 360. Check which one your agreement states.