Question

In what time will Rs.8000 amounts to Rs.9261 at 5% per annum ,interest compounded annually

Answer 1

P = 8000      r = 5% = 0.05    n = unumber of years
9261 = 8000 (1 + 0.05)^n
9261 / 8000  =  1.05 ^n
take logarithms
log 9261 /8000  =  n  log 1.05
 n  =  (1/ log 1.05)  log  1.157  years  = 2.99  = 3 years nearly

Answer 2

A = P $( 1 + \frac{r}{n}) ^{n.t}$

Where, A= amount, P = Principal, n= no.of times it is compounded (here n=1), r=5% , t=?

Now putting the values,

9261 = 8000 $(1 + \frac{5}{100}) ^{1.t}$

$\frac{9261}{8000}$ = $(\frac{21}{20} ) ^{t}$

$(\frac{21}{20}) ^{3}$ = $(\frac{21}{20}) ^{t}$

Now comparing both sides,
we get,
t = 3 years (Answer).