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There is 60% increase in an amount in 6 years at simple interest. What will be the compound interest of Rs.12,000 after 3 years at the same rate?

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Rs. 2,160

Rs. 3,120

Rs. 3,972

Rs. 6,240

answer is C.

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Detailed Solution

Concept: Using formula for simple, final amount and compound interest which are,

S . I = \frac{P \times R \times T}{100}

C . I = A - P

and

A {= P (1 + \frac{R}{100})}^{N}

respectively.
where,

P = Initial amount

A = Final amount

R = Rate

T = Time

N = No . of years

Given is that:
There is a 60% increase in the amount in 6 years.
Therefore, Simple interest (S.I) will be 60% of the Initial amount P.

60 % of P

S . I = \frac{60 P}{100}

Now, the formula for S.I is:

S . I = \frac{P \times R \times T}{100}

where,

T = 6 years

Putting the values in, we get:

S . I = \frac{P \times R \times 6}{100}

S . I = \frac{6 PR}{100}

Now, the two values of S.I obtained will eventually be equal. Equating the two:

\frac{60 P}{100} = \frac{6 PR}{100}

∴ R = 10

Now, we have to find the compound interest after 3 years at the same rate.
Putting all the known values in the formula for of final amount A, we get:

A {= P (1 + \frac{R}{100})}^{N}

{= 12, 000 (1 + \frac{10}{100})}^{3}

{= 12, 000 \times (\frac{110}{100})}^{3}

{= 12, 000 \times (\frac{11}{10})}^{3}

= 12, 000 \times \frac{1331}{1000}

= 12 \times 1331

= 12 \times 1331

A = Rs . 15, 972

Therefore, C.I will be:

C . I = A - P

C . I = Rs . (15, 972 - 12, 000)

C . I = Rs . 3, 972

Hence, the correct option is 3.

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