Question

RS 2700 BECOMES RS 4800 AT A CERTAIN RATE OF INTEREST COMPOUNDED ANNUALLY IN 3 YEAR. FIND THE AMOUNT AT THE END OF 4.5 YEAR SOLVE THIS

Answer 1

Given:

Principal, P = Rs. 2700

Amount, A = Rs. 4800

Time period, n = 3 years

To find:

The amount at the end of 4.5 years

Formula to find the amount in the compound interest:

$\boxed{\bold{A = P[1 + \frac{R}{100} ]^n}}$

Solution:

Since 2700 becomes 4800 in 3 years at a certain rate of interest, therefore using the formula, we get

$4800 = 2700 [1 + \frac{R}{100} ]^3$

$\implies \frac{4800}{2700} = [1 + \frac{R}{100} ]^3$

$\implies \frac{48}{27} = [1 + \frac{R}{100} ]^3$ ....... (i)

Now, using the formula again we will find the amount at the end of 4.5 years:

$A = 2700\times [1 + \frac{R}{100}]^4^.^5$

$\implies A = 2700\times [1 + \frac{R}{100}]^3[1+ \frac{R}{100} ]^\frac{3}{2}$

$\implies A = 2700\times [1 + \frac{R}{100}]^3\sqrt{[1+ \frac{R}{100} ]^3}$

substituting from (i), we get

$\implies A = 2700\times \frac{48}{27}\times \sqrt{\frac{48}{27} }$

$\implies A = 2700\times \frac{48}{27}\times \frac{6.928}{5.196}$

$\implies A = \frac{897868.8}{140.292}$

$\implies \bold{A = Rs.\:6400}$

Thus, the amount at the end of 4.5 years is Rs. 6400.

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