Question

A sum of money becomes $\frac{8}{5}$th of itself in $5$ years at certain a rate of simple interest. Find the rate of interest.

Answer 1

Let the Initial principle amount $=P$

After $5$ years the amount received $=\left(\frac{8}{5}\right)P$

As the interest applicable is simple interest, the total interest is Final amount received $-$ Initial principle amount.

Interest amount for $5$ years $=\left(\frac{8}{5}\right)P-P$

Interest amount for $5$ years $=\left(\frac{3}{5}\right)P$

With simple interest, interest amount every year is the same.

Thus interest for one year $=$ Interest for $5$ years $÷5$

Interest for one year $=\frac{\left(\frac{3}{5}\right)P}{5}$

Interest for one year $=\frac{3}{25}P$

Simple Rate of interest per year $=\frac{AmountofInterestreceivedperyear}{InitialPrincipleamount}$ $\times 100\%$

$\therefore$ Rate of interest per year $=(\left(\frac{3}{25}\right)P÷P)\times 100\%$

$\therefore$ simple rate of interest $=\frac{3}{25}\times 100\%$

$\therefore$ Simple Rate of interest $=12\%$