Question

What sum of money will amount to Rs. 27,783 in one and a half years at 10% per annum compounded half yearly ?

Answer 1

Given that

A = Rs 27,783

R = 10 % p.a.

T = 1 + $\frac{1}{2}$ years

= 2+$\frac{1}{2}$ years

= $\frac{3}{2}$ years

Solution

When the interest is compounded half - yearly

$A=P(1+\frac{R}{200}{)}^{\frac{3}{2}}$ × 2

$\to 27,783=P(1+\frac{10}{200}{)}^3$

$\to 27,783=P\times (\frac{(200+10}{200}{)}^3$

$\to 27,783=P\times (\frac{210}{200}{)}^3$

$\to 27,783=P\times (\frac{21}{20}{)}^3$

$\to 27,783=P\times \frac{9,261}{8,000}$

$\to P=27,783\times \frac{8,000}{9,261}$

$\to P=₹24,000$