# (solved)Question 12 SSC-CGL 2020 March 3 Shift 2

A certain amount yields an interest of Rs. 1200 when invested for 3 years at a simple interest of 5%. Calculate the interest if the interest had, instead, been compounded annually at the same rate?
(Rev. 20-Nov-2022)

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### Question 12SSC-CGL 2020 Mar 3 Shift 2

A certain amount yields an interest of Rs. 1200 when invested for 3 years at a simple interest of 5%. Calculate the interest if the interest had, instead, been compounded annually at the same rate?

### Solution in Short

Useful Short Cut: Difference between the compound and simple interest at a rate of R% for 3 years is = [R(3 + R)/3] x SI, where SI is the simple interest after 3 years.

Given $\displaystyle R = 5\%$

SI for 2 years given $\displaystyle 1200$ Rs.

Diff. between SI and CI after 3 yrs:

$\displaystyle = \frac{0.05 \times (3 + 0.05)}{3} \times 1200 = 61$

$\displaystyle \therefore CI = SI + 61$

$\displaystyle = 1200 + 61 = 1261\:\underline{Ans}$

### Useful Shortcuts for 2 years

Difference between SI and CI on a principle P after 2 years:

$\displaystyle \text{(CI - SI)}_2 = P \times R^2$

If SI after 2 years is $\displaystyle I$, then

$\displaystyle \text{(CI - SI)}_2 = \frac{R}{2} \times I$

### Useful Shortcuts for 3 years

Difference between SI and CI on a principle P after 3 years:

$\displaystyle \text{(CI - SI)}_3 = P \times R^2 \times (R + 3)$

If SI after 3 years is $\displaystyle I$, then

$\displaystyle \text{(CI - SI)}_3 = \frac{R \times (R + 3)}{3} \times I$