Question

What sum will amount to Rs. 4913 in 18 months, if the rate of interest is $12\frac{1}{2}\%$ per annum, compounded half-yearly.

Answer 1

Amount (A) = Rs. 4913
Rate (R) $=Rs.12\frac{1}{2}\%=\frac{25}{2}\%$ p.a or $\frac{25}{4}\%$ half-yearly.
Period (n) = 18 months or 3 half years.
$\therefore A=P{(1+\frac{R}{100})}^n$
or $P=A÷{(1+\frac{R}{100})}^n$
$=Rs.4913÷{(1+\frac{25}{4\times 100})}^3$
$=Rs.4913÷{\left(\frac{17}{16}\right)}^3$
$=Rs.4913\times {\left(\frac{16}{17}\right)}^3=Rs.\frac{4913\times 16\times 16\times 16}{17\times 17\times 17}$
$=Rs.4096$
$\therefore$ Principal = Rs. 4096