Question

Man invested rs. 50000 for 3 years at the compound interest rate of 10% per annum. after 2 years the rate of interest was raised to 10%. (a) find the total interest earned by him. (b) find the amount he received after 3 years. (c) find the amount he received after 10 years if the compound interest rate is of 15%.

Answer 1

$\underline { \blue { Case \:1 : }}$

$Principal (P) = Rs\:50000,\\Time (T) = 2 \:years$

$Rate \:of \: interest (R) = 10\% ,\:p.a$

$Conversion \:period (n) = 2$

$Let \: the \: Amount \: after \:2 \: years = A$

$\boxed { \pink { A = P\big( 1 + \frac{R}{100}\big)^{n} }}$

$A = 50000\big( 1 + \frac{10}{100}\big)^{2} \\= 50000 \times (1.1)^{2} \\= Rs\:60500\: --(1)$

$\underline { \blue { Case \:2 : }}$

$Principal (P) = Rs\:60500,\\Time (T) = 1 \:years$

$Rate \:of \: interest (R) = 20\% ,\:p.a$

$\boxed{\pink { Amount = P\big(1 + \frac{TR}{100}\big) }}$

$Amount = 60500\big( 1 + \frac{1\times 20}{100}\big) \\= 60500\big( 1+ \frac{1}{5}\big)\\= 60500 \times \frac{6}{5} \\= Rs\:72600\: --(2)$

$a) Total \: interest \: earned \:by \:him\\ = (2)- Investment \\=Rs\: 72600 - Rs\:50000\\= Rs\:22600$

$\underline { \blue { Case \:3: }}$

$Principal (P) = Rs\:50000,\\Time (T) = 15 \:years$

$Rate \:of \: interest (R) = 10\% ,\:p.a$

$Conversion \:period (n) = 15$

$Let \: the \: Amount \: after \:15\: years = A$

$A = 50000\big( 1 + \frac{10}{100}\big)^{15} \\=</p><p>Rs\:50000\times (1.1)^{15}$

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