Question

a sum of rupees 15000 amounts to rupees 16537.50 in X years at 5% per annum compound interest find x​

Answer 1

Answer:-

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Given:

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▪︎Principal(P) = Rs.15000

▪︎Amount(A) = Rs.16537.50

▪︎Rate% compound yearly(r) = 5%

▪︎Time(t) = x

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To Find:

▪︎Value of x

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Solution:

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According to given conditions;

$\sf{}Amount = Rs.16537.50$

$\sf{}\implies P × {(1+\frac{r}{100})}^{t} = 16537.50$

$\sf{}\implies 15000 × {(1+\frac{5}{100})}^{x} = 16537.50$

$\sf{}\implies {(\frac{105}{100})}^{x} = \frac{16537.50}{15000}$

$\sf{}\implies {(1.05)}^{x} = 1.025$

$\sf{}\implies {1.05}^{x} = \sqrt{1.05 × 1.05}$

$\sf{}\implies {\cancel{(1.05)}}^{x} = {\cancel{(1.05)}}^{2}$

$\sf{}\implies x = 2$

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$\boxed{\pink{\bf{\therefore Value\ of\ x\ is\ 2 years}}}$

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Formula to be remembered:-

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▪︎$\bf{}Amount = P × {(1+\frac{r}{100})}^{t}$

▪︎$\bf{}C.I. = Amount - Principal$