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Dima020 [189]
3 years ago
6

A certain sum quadruples in 3 years at compound interest, interest being compounded annually. In how many years will it become 6

4 time itself?
Mathematics
1 answer:
Alex777 [14]3 years ago
5 0

<u>ANSWER:  </u>

In 9 years, amount becomes 64 times of itself.

<u>SOLUTION: </u>

Given, a certain sum quadruples in 3 years at compound interest, interest being compounded annually.  

We know that, When interest is compound annually:

\text { Amount }=P\left(1+\frac{R}{100}\right)^{n}

Given that,

Principal = Rs.100%

Amount = Rs.400

Rate = r%

Time = 3 years

By substituting the values in above formula, we get,

400=100 \times\left[1+\left(\frac{R}{100}\right)\right]^{3}

4=1\left[1+\left(\frac{R}{100}\right)\right]}^{3} --- eqn 1

If sum become 64 times in the time n years then,

64=\left(1+\left(\frac{R}{100}\right)\right)^n

4^{3}=\left(1+\left(\frac{R}{100}\right)\right)^{n} --- eqn 2

Using equation (1) in (2), we get

\begin{array}{c}{\left(\left[1+\left(\frac{R}{100}\right)\right]^{3}=\left(1+\left(\frac{R}{100}\right)\right)^{2}\right.} \\ {\left[1+\left(\frac{R}{100}\right)\right]^{9}=\left(1+\left(\frac{R}{100}\right)\right)^{n}}\end{array}

Thus, n = 9 years by comparing on both sides.

Hence, in 9 years, amount becomes 64 times of itself.

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