Question

What sum of money lent at $6.5\%$ per annum will produce the same interest in $4$ years as $Rs.7500$ will produce at $5\%$ p.a in the same time period.

Answer 1

For simple interest:

$SI=\frac{P\ast N\ast r}{100}$

$\because S{I}_1=S{I}_2$

$\frac{P\ast 4\ast 6.5}{100}=\frac{7500\ast 4\ast 5}{100}$

$\therefore P=\frac{7500\ast 5}{6.5}$

$P=5769.23\approx 5770$

For compound interest:

$CI=P[{(1+\frac{r}{100})}^n-1]$

$\because C{I}_1=C{I}_2$

$P[{(1+\frac{6.5}{100})}^4-1]$$=7500[{(1+\frac{5}{100})}^4-1]$

$\therefore P=\frac{1616.297}{0.2865}$

$P=5642.18\approx 5643$