Question

What is the, difference between the compound interests on Rs. 5,000 for $1\frac{1}{2}$ years at 4% per annum compounded yearly and half-yearly?

• A. Rs. 2.04
• B. Rs. 3.06
• C. Rs. 4.80
• D. Rs. 8.30

Answer 1

The correct option is B Rs. 3.06

In the first case, The amount=A=Rs5000, rate=4%,

time= yr @ 4% and $\frac{1}{2}$ @2%

( rate becomes half in case the time is half year).

So the interest after 1 yr$=Rs\frac{5000\times 4\times 1}{100}=Rs200.$.

$\therefore$ The amount $=Rs(5000+200)=Rs5200\text{and rate}=2\%.$

So the interest for half year=$Rs\frac{5200\times 2\times 1}{100}=Rs\mathrm{102.98.}$.

$\therefore$ The total interest $=Rs(200+102.98)=Rs\mathrm{302.98.}$

In the second case, time slot=3 half yrs. rate=2%.

$\therefore Amount=principal\times {(1+rate)}^{time}=Rs5000\times {(1+\frac{4}{100})}^3=Rs\mathrm{5306.04.}\therefore I=Rs(5306.04-5000)=Rs\mathrm{306.04.}$

So the difference in 2 interests $=Rs(306.04-302.98)=Rs.3.06.$