Question

What sum invested for 1 and a half years compounded half-yearly at the rate of $4\%$ p.a will amount to $1,32,651$?

Answer 1

Let the principle be $Rs.P$

Time$=1$ and half year$=18$ months$=3$ half year

Rate of interest $=4\%$

Rate is compounded half yearly,

So, $\frac{4\%}{2}=2\%$

amount $=P{\left(\frac{100+r}{100}\right)}^t$

$132651=P{\left(\frac{100+2}{100}\right)}^3$

$132651=P{\left(\frac{51}{50}\right)}^3$

$P=\frac{132651\times 50\times 50\times 50}{51\times 51\times 51}$

$P=125000$

Therefore$,$ sum $=Rs.=125000$