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A sum of Rs. $12, 000$ is invested for $3$ years at $18$ % per annum compound interest. What is the interest for the third year?

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Rs.

2700

Rs.

2800

Rs.

2900

Rs.

3000

answer is D.

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Detailed Solution

Given, a sum of Rs.

12, 000

is invested for

3

years at

18

% per annum compound interest.
We know that

A = P (1 + \frac{r}{n})^{nt}

where P = principal amount, t = time, r = interest rate and n is the number of times interest is compounded in a year (Here n = 1).
So, the amount after two years =

12000 (1 + \frac{18}{100})^{2}

\Rightarrow

The amount after two years =

12000 (1.18)^{2}

\Rightarrow

The amount after two years = Rs. 16708.8
We know that interest =

\frac{PTR}{100}

, where P = principal amount, T = time, R = interest rate.
Here P = Rs. 16708.8, T = 1 year and R = 18%.

\Rightarrow

Interest in third year =

\frac{16708.8 (1) (18)}{100}

\Rightarrow

Interest in third year = 3007.584

\Rightarrow

Interest in third year

\sim

Rs. 3000
Hence, option 4 is correct.

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