Question

Rajeev took 27200 as a loan which along with interest is to be repaid in two equal annual installments If the rate of interest 12½% is compounded annually then the value of each installment

A) 15600

B) 16200

C) 12400

D) 18700​

Answer 1

$Let \: the \: value \: of \: each \: instalment$

$be \: Rs \: x$

$Loan = Rs \: 27200$

$Rate \:of \:interest (r)$

$= 12 \frac{1}{2} \%$

$= \frac{25}{2}\%$

$Therefore , we \:have$

$\frac{x}{\Big( 1 + \frac{r}{100}\Big)} + \frac{x}{\Big( 1 + \frac{r}{100}\Big)^{2}} = 27200$

$\frac{x}{\Big( 1 + \frac{25}{2 \times 100}\Big)} + \frac{x}{\Big( 1 + \frac{25}{2\times 100}\Big)^{2}} = 27200$

$\implies \frac{x}{\Big( 1 + \frac{25}{200}\Big) } + \frac{x}{\Big( 1 + \frac{25}{200}\Big)^{2}}= 27200$

$\implies \frac{x}{\frac{225}{200} } + \frac{x}{\Big( \frac{225}{200}\Big)^{2} } = 27200$

$\implies \frac{200x}{225} + \frac{40000x}{225^{2}} = 27200$

$\implies \frac{45000x + 40000x}{50625} = 27200$

$\implies \frac{ 85000x}{50625} = 27200$

$\implies x = 27200 \times \frac{ 50625}{85000}$

$\implies x = Rs \:16200$

Therefore.,

$\red{ Value \:of \:each \: instalment }$

$\green { = Rs \:16200 }$

$Option \: \pink { ( B ) } \: is \: correct.$

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