Formula

Two-year difference between compound and simple interest

Arithmetic • Interest • Difference of SI and CI

Formula

CI - SI = P (\frac{r}{100})^{2}

On a principal

P

r %

per annum compounded annually, the two-year difference is

CI - SI = P (\frac{r}{100})^{2}

, because it is exactly one year's interest on the first year's interest.

How to use it

1Given the difference and the rate, divide to recover the principal in one step.
2Remember why it works - the only interest simple interest misses in two years is the interest on year one's interest - and the formula never has to be memorised.
3For three years the difference is $P (\frac{r}{100})^{2} (\frac{r}{100} + 3)$ , not the square formula again.

Worked example

The difference between compound and simple interest on a sum for

2

years at

10%

per annum is Rs.

60

. Find the sum.

Step-by-step

1
$P (\frac{10}{100})^{2} = 60$
Why: Apply the two-year difference formula with $r = 10$ .
2
$\frac{P}{100} = 60 \Rightarrow P = 6000$

Answer

Rs.

6000

Watch out

It holds for TWO years only, and only when the compounding period is the year the rate is quoted in. Half-yearly compounding needs the rate halved and the number of periods doubled before any of this applies.

Builds on

Percentage change as a multiplier

Also known as

difference between CI and SI, CI minus SI for 2 years, simple and compound interest difference, P(r/100)^2

Two-year difference between compound and simple interest

Formula

Worked example

Appears in past papers

2017 (II)

2017 (I)