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

Question #156352

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.


1
Expert's answer
2021-02-02T06:27:07-0500

Let the elapsed time be nn years

For it renewed after every half year it will be 2n2n


A=8500A=8500

P=850P=850

i=21i=21%

A=p(1+i)A=p(1+i)2n


8500=850(1+218500=850(1+21%))2n


8500750=(1+21100)\frac{8500}{750}=(1+\frac{21}{100})2n


Taking loglog on both sides,

log(8500850)=log(1+21100)log(\frac{8500}{850}) =log(1+\frac{21}{100})2n


log(8500850)=2nlog(1+21100)log(\frac{8500}{850}) =2nlog(1+\frac{21}{100})


log(8500850)=2nlog(121100)log(\frac{8500}{850}) =2n log(\frac{121}{100})


1=2n(0.08279)1= 2n(0.08279)


n=12×0.08279n=\frac{1}{2×0.08279}


n=6.0393n=6.0393


n=6n=6 years approximately



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