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In what time will Rs. $15, 000$ yield Rs. $4965$ as compound interest at $10$ % per year compounded annually?

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3

years

2

years

1

years

4

years

answer is A.

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Detailed Solution

Given, Rs.

15, 000

yield Rs.

4965

as compound interest at

10

% per year compounded annually.
So, the final amount is 15000 + 4965 = Rs 19965.
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).
Substitute respective values in the formula.

\Rightarrow 19965 = 15000 (1 + \frac{10}{100})^{t}

\Rightarrow 1 . 1^{t} = \frac{19965}{15000}

\Rightarrow 1 . 1^{t} = 1.331

\Rightarrow tlog (1.1) = \log (1.331)

\Rightarrow t = \frac{\log 1.1}{\log 1.331}

\Rightarrow t = 3

So, after 3 years Rs.

15, 000

yields Rs.

4965

.
Hence, option 1 is correct.

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In what time will Rs. 15,000 yield Rs. 4965 as compound interest at 10% per year compounded annually?

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In what time will Rs. $15, 000$ yield Rs. $4965$ as compound interest at $10$ % per year compounded annually?