(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. 31-Oct-2024)

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Question 12
SSC-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 R=5%\displaystyle R = 5\%

SI for 2 years given 1200\displaystyle 1200 Rs.

Diff. between SI and CI after 3 yrs:

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

CI=SI+61\displaystyle \therefore CI = SI + 61

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

Useful Shortcuts for 2 years

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

(CI - SI)2=P×R2\displaystyle \text{(CI - SI)}_2 = P \times R^2

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

(CI - SI)2=R2×I\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:

(CI - SI)3=P×R2×(R+3)\displaystyle \text{(CI - SI)}_3 = P \times R^2 \times (R + 3)

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

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

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