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.

Start with this

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.

The formula and what each letter means: the rules

Worked example

Find the simple interest on Rs 8,000 at 7.5% a year for 3 years.

1. SI = 8000 × 7.5 × 3 / 100.
   Why: Put the numbers in.
2. = 80 × 22.5 = 1,800.

Answer: 1800

Worked example

At what rate will Rs 2,500 earn Rs 600 simple interest in 4 years?

1. R = 100 × 600 / (2500 × 4).
   Why: Rearranged formula.
2. = 60000 / 10000 = 6%.

Answer: 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.

Worked example

A sum doubles in 8 years at simple interest. In how many years will it become 5 times?

1. Doubling: interest = P in 8 years, so R = 12.5%.
   Why: R × 8 = 100.
2. 5 times: interest = 4P, so R × T = 400.
   Why: n - 1 = 4.
3. T = 400 / 12.5 = 32 years.

Answer: 32

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.

Worked example

A sum amounts to Rs 7,000 in 4 years and Rs 8,500 in 7 years at simple interest. Find the principal and the rate.

1. 3 extra years give 1,500, so one year = 500.
   Why: Simple interest is the same every year.
2. 4 years = 2,000, so P = 7000 - 2000 = 5,000.
3. R = 500/5000 × 100 = 10%.

Answer: P = Rs 5,000 and R = 10%

Shortcut: Two totals, two times

Use it when: 'Becomes 7,200 in 3 years and 8,400 in 5 years'.

1. 2 years of interest = 1200 → 600 a year.
2. P = 7200 - 3 × 600.

Two totals, two times: try it

As above. Principal?

1. 7200 - 1800.

Answer: Rs 5,400

Your turn 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%?

1. Alligation on rates: overall rate 9.5%.
2. (12 - 9.5):(9.5 - 8) = 2.5 : 1.5 = 5:3.
3. 5/8 × 12000.

Answer: Rs 7,500

Your turn medium

At what rate will SI be 3/8 of the principal in 6 years?

1. R × 6 = 37.5.

Answer: 6.25%

Your turn hard

A sum becomes 3/2 of itself in 10 years at SI. Rate?

1. SI = 1/2 of P in 10 years.

Answer: 5%

Your turn hard

SI on a sum for 3 years at 12% is Rs 5,400 less than the sum. The sum?

1. SI = 0.36P = P - 5400 → 0.64P = 5400.

Answer: Rs 8,437.50

Recap

• 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

Now practise

6 questions with full solutions.

Open practice Back to the lesson