Simple Interest
SI is the same amount every year. If you know two year-end totals, their gap divided by the years between is one year's interest.
Why this topic matters
You lend Rs 1,000 at 10% a year. Every year you get Rs 100, the same Rs 100, because simple interest is always on the original amount.
Simple interest is one formula, SI = P R T / 100, used in four directions: find the interest, the principal, the rate or the time.
The formula and what each letter means
P is the principal (the money lent). R is the rate per year in %. T is the time in years. SI = P × R × T / 100.
Amount A = P + SI: what you get back at the end.
Time in months? Divide by 12. 9 months = 3/4 year.
- SI = 8000 × 7.5 × 3 / 100.Put the numbers in.
- = 80 × 22.5 = 1,800.
- R = 100 × 600 / (2500 × 4).Rearranged formula.
- = 60000 / 10000 = 6%.
Doubling and tripling
If a sum doubles, the interest equals the principal: SI = P, so R × T = 100.
If it becomes n times, SI = (n - 1) P, so R × T = 100 (n - 1). A sum that doubles in 8 years (R = 12.5%) becomes 4 times in 24 years, not 16.
- Doubling: interest = P in 8 years, so R = 12.5%.R × 8 = 100.
- 5 times: interest = 4P, so R × T = 400.n - 1 = 4.
- T = 400 / 12.5 = 32 years.
Two amounts, two times
'A sum amounts to Rs 1,120 in 2 years and Rs 1,200 in 3 years.' The extra Rs 80 is one year's interest. Two years' interest = 160, so P = 1120 - 160 = 960.
- 3 extra years give 1,500, so one year = 500.Simple interest is the same every year.
- 4 years = 2,000, so P = 7000 - 2000 = 5,000.
- R = 500/5000 × 100 = 10%.
Formula summary
Shortcuts and tricks
Two totals, two times
Use it when: 'Becomes 7,200 in 3 years and 8,400 in 5 years'.
- 2 years of interest = 1200 → 600 a year.
- P = 7200 - 3 × 600.
- 7200 - 1800.
Before you move on, you should be able to...
- use SI = PRT/100 to find any one letter
- solve doubling and n-times questions with RT = 100(n - 1)
- get P and R from two amounts at two times
Practice questions (6)
Try each one before opening the solution. Or practise them one by one so your score is saved.
easy SI on Rs 5,000 at 8% for 3 years?
- 5000 × 8 × 3/100.
Answer: Rs 1,200
easy A sum doubles in 8 years at SI. In how many years will it triple?
- Rate 12.5%.
- Triple needs 200% interest → 16 years.
Answer: 16 years
medium Rs 12,000 is lent partly at 8% and partly at 12% SI. Total interest after 1 year is Rs 1,140. Amount lent at 8%?
- Alligation on rates: overall rate 9.5%.
- (12 - 9.5):(9.5 - 8) = 2.5 : 1.5 = 5:3.
- 5/8 × 12000.
Answer: Rs 7,500
medium At what rate will SI be 3/8 of the principal in 6 years?
- R × 6 = 37.5.
Answer: 6.25%
hard A sum becomes 3/2 of itself in 10 years at SI. Rate?
- SI = 1/2 of P in 10 years.
Answer: 5%
hard SI on a sum for 3 years at 12% is Rs 5,400 less than the sum. The sum?
- SI = 0.36P = P - 5400 → 0.64P = 5400.
Answer: Rs 8,437.50
Class plan (2 hours, for trainers)
A tested order for teaching this topic in one 2-hour session. Present mode follows the same order.
| 10 min | Warm-up. |
| 30 min | The formula in four directions. |
| 25 min | Doubling, tripling. |
| 20 min | Two amounts at two times. |
| 30 min | Practice set. |
| 5 min | Recap. |