Question

Ashok invests a certain sum of money at $20$% per annum, compounded yearly. Geeta invests an equal amount of money at the same rate of interest per annum compounded half-yearly. If Geeta gets Rs. $33$ more than Ashok in $18$ months, calculate the money invested.

• A. $5000$
• B. $3000$
• C. $300$
• D. $500$

Answer 1

Answer: (B)

$3000$

Let $P$ be the principle, $R=20\%$, $T=18months=1.5years$,

for Ashok (compounded yearly)

$\Rightarrow$Amount $=p{(1+\frac{R}{100})}^T$

$\Rightarrow$$A_1=P{(1+\frac{20}{100})}^{1.5}=1.32P$

for Geeta (compounded half-yearly)

$\Rightarrow$$A_2=P{(1+\frac{R}{200})}^{2T}=P{(1+\frac{20}{200})}^{2\times 1.5}$

$\Rightarrow$$A_2=1.331P$

Given $A_1-A_2=33⟹(1.331-1.32)P=33$

$⟹P=3000$