Question

if rs 21870 yields rs 8130 compound interest if borrowed at 11×1/19 % find time

Answer 1

SOLUTION

GIVEN

Rs 21870 yields Rs 8130 compound interest if borrowed at $\displaystyle \sf{11 \frac{1}{9} \: \%}$

TO DETERMINE

The time

EVALUATION

Here

Total amount

= Rs ( 21870 + 8130 )

= Rs 30000

Principal = P = Rs 21870

Rate of interest

$\displaystyle \sf{ = r \ \% = 11 \frac{1}{9} \: \%}$

Let time = n years

So by the given condition

$\displaystyle \sf{ 30000 = 21870 \times { \bigg( 1 + \frac{ \frac{100}{9} }{100} \bigg)}^{n} }$

$\displaystyle \sf{ \implies \frac{30000}{21870} = { \bigg( 1 + \frac{ 1}{9} \bigg)}^{n} }$

$\displaystyle \sf{ \implies \frac{30000}{21870} = { \bigg( \frac{ 10}{9} \bigg)}^{n} }$

$\displaystyle \sf{ \implies \frac{21870}{30000} = { \bigg( \frac{ 9}{10} \bigg)}^{n} }$

$\displaystyle \sf{ \implies {( 0.9 )}^{n} = 0.729 }$

$\displaystyle \sf{ \implies {( 0.9 )}^{n} = {(0.9)}^{3} }$

$\displaystyle \sf{ \implies n = 3 }$

Hence the required time = 3 years

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