Question

In how many years will a sum of Rs. 15,625 at 8% per annum compounded semi annually become Rs. 17,576
a) 2 1/3 years
b) 2 years
c) 1 1/2 years
d) 1 year ​

Answer 1

Answer:

Given:-

P=Rs 15,625

R=8%(8/2=4%) as it is compounded semi annually

T=?

A=Rs 17576

Since,

$A=P {(1 + \frac{r}{100} })^{n}$

$Rs \: \: 17576 = Rs \: \: 15625 {(1 + \frac{4}{100}) }^{n}$

$Rs \: \: 17576 = Rs \: \: 15625 {( \frac{104}{100}) }^{n}$

$\frac{Rs \: \: 17576}{Rs \: \: 15625} = ( { \frac{26}{25} )}^{n}$

$( { \frac{26}{25} })^{3} = ({ \frac{26}{25} })^{n}$

n=3

n=number of conversions

Hence,

$t = \frac{3}{2}$

$t = 1 \frac{1}{2} \: \: years$

Hence,

Option c is correct.