Question

find the sum that yields an interest of ₹170 after 2 years at the rate of 12 1/2 pa interest being compounded annually

Answer 1

Given:

Interest earned is ₹$170$, rate of interest is $12\frac{1}{2}\%$ p.a. and number of years is $2$ years.

To find:

Sum on which the given interest is earned.

Solution:

Amount compounded annually is calculated by

$A=P(1+\frac{r}{100} )^{n}$,    ---------------------------------$(1)$

where $P=$ sum amount,

$A=$ amount after compounding,

$r=$ rate of interest, and

$n=$ number of years.

Amount is sum of sum amount and interest.

Here, $A=P+170$             (It is given that interest earned is ₹$170$)

From $(1)$,

$P+170=P(1+\frac{25}{200} )^{2}$

$P+170=P(1+\frac{1}{8} )^{2}$

$\\P+170=P(\frac{9}{8} )^{2}$

$\\P+170=\frac{81}{64} P$

$\frac{17}{64}P=170$

⇒$P=$ ₹$640$

Hence, sum that yields an interest of ₹$170$ after $2$ years at the rate of  $12\frac{1}{2}\%$ p.a. interest being compounded annually is ₹640.