Answer to Question #156352 in Financial Math for Mahfuz Hossain Patwary

Question

A man borrows 850 taka from bank. The bill is renewed after every half year at an increase of 21% . After haw much time amount will become 8500 taka.

Answer 1

Let the elapsed time be $n$ years

For it renewed after every half year it will be $2n$

$A=8500$

$P=850$

$i=21$%

$A=p(1+i)$²ⁿ

$8500=850(1+21$%$)$²ⁿ

$\frac{8500}{750}=(1+\frac{21}{100})$²ⁿ

Taking $log$ on both sides,

$log(\frac{8500}{850}) =log(1+\frac{21}{100})$²ⁿ

$log(\frac{8500}{850}) =2nlog(1+\frac{21}{100})$

$log(\frac{8500}{850}) =2n log(\frac{121}{100})$

$1= 2n(0.08279)$

$n=\frac{1}{2×0.08279}$

$n=6.0393$

$n=6$ years approximately