Question

16.At what rate percent per annum would Rs:7200 amount to Rs: 9468 in 9/2 years

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Answer 1

$\large\underline{\sf{Solution-}}$

Given that,

• Principal, P = Rs 7200

• Amount, A = Rs 9468

• Time, T = 4.5 years

Let rate of interest be R % per annum.

We know,

Simple Interest S.I. is given by

$\rm :\longmapsto\:S.I. = Amount - Principal$

$\rm :\longmapsto\:S.I. = 9468 - 7200$

$\bf\implies \:S.I. = Rs \: 2268$

Now,

We know that,

Simple Interest on a certain sum of money Rs P at the rate of R % per annum invested for T years is

$\rm :\longmapsto\:S.I. = \dfrac{P \times R \times T}{100}$

$\bf\implies \:R = \dfrac{S.I. \times 100}{P \times T}$

$\rm :\longmapsto\:R = \dfrac{2268 \times 100}{7200 \times 4.5}$

$\bf\implies \:R = 7\% \: per \: annum$

Additional Information :-

Amount on a certain sum of money Rs P at the rate of R % per annum compounded annually, invested for T years is

$\tt{\implies Amount=P\bigg(1+\dfrac{R}{100}\bigg)^{T}}$

Amount on a certain sum of money Rs P at the rate of R % per annum compounded half yearly, invested for T years is

$\tt{\implies Amount=P\bigg(1+\dfrac{R}{200}\bigg)^{2T}}$

Amount on a certain sum of money Rs P at the rate of R % per annum compounded quarterly, invested for T years is

$\tt{\implies Amount=P\bigg(1+\dfrac{R}{400}\bigg)^{4T}}$