[2 Mark Question Answer]

Question 12 Marks

A certain sum amounts to $Rs. 5,292$ in two years and $Rs. 5,556.60$ in three years$,$ interest being compounded annually. Find$: $the original sum.

Answer

Let the sum of money $ = Rs. 100$
Interest on it for $1^{\text {st }}$ year $=5 \%$ of $Rs. $$100=$$Rs. 5$
$\Rightarrow$ Amount in one year$= Rs.$$100+Rs.$ $5=$$Rs. 105$
Similarly$,$ amount in two years $=$ $Rs.105+5 \%$ of $Rs. 105$
$=$ $Rs. 105+ Rs. 5.25$=$Rs. 110.25$
When amount in two years is $Rs. 110.25 , \sum = Rs. 100$
$\Rightarrow$ When amount in two years is $Rs. 5,292,$
$\text { sum }=\text { Rs. } \frac{100 \times 5,292}{110.25}=\text { Rs. } 4,800 \text {. }$

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Question 22 Marks

A certain sum amounts to $ Rs. 5,292$ in two years and $ Rs. 5,556.60$ in three years$,$ interest being compounded annually. Find$ :$ the rate of interest.

Answer

Amount in two years$= Rs. 5,292$
Amount in three years $= Rs. 5,556.60$
Difference between the amounts of two successive years
$=\text { Rs. } 5,556.60 \text { - Rs. } 5,292=\text { Rs. } 264.60$
$\Rightarrow Rs. 264.60$ is the interest of one year on $Rs. 5,292$
$\therefore \text { Rate of interest }=\text { Rs. } \frac{100 \times \mathrm{I}}{\mathrm{P} \times \mathrm{T}} \%$
$ =\frac{100 \times 264.60}{5,292 \times 1} \%$
$ =5 \%$

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Question 32 Marks

A certain sum of money is put at compound interest$,$ compounded half$-$yearly. If the interest for two successive half $-$ years are $Rs. 650 $ and $Rs. 760.50;$ find the rate of interest.

Answer

$\because$ Difference between the $C.I.$ of two successive half$-$years
$=\text { Rs. } 760.50 \text { - Rs. } 650=\text { Rs. } 110.50$
$\Rightarrow Rs. 110.50 $ is the interest of one half$-$year on $Rs. 650$
$\therefore \text { Rate of interest }=\text { Rs. } \frac{100 \times \mathrm{I}}{\mathrm{P} \times \mathrm{T}}\%$
$ =650 \times \frac{1}{2} \%$
$ =34 \%$

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Question 42 Marks

A sum is invested at compound interest $,$ compounded yearly $. $If the interest for two successive years is $Rs. 5,700$ and $Rs. 7,410.$ calculate the rate of interest$.$

Answer

Rate of interest $=\frac{\text { Difference in the interest of the two consecutive periods } \times 100}{\text { C.I. of preceeding year } \times \text { Time }} \%$
$=\frac{(7410-5700) \times 100}{5700 \times 1} \%$
$=30 \%$

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Question 52 Marks

A man invest $ 5,600$ at $14\%$ per annum compound interest for $ 2$ years. Calculate $:$The interest for the first year.

Answer

For $1^{\text {st }}$ years
$P=\text { Rs. } 5600$
$ R=14 \%$
$ T=1 \text { year }$
$ =\frac{5600 \times 14 \times 1}{100}$
$=\text { Rs. } 784$

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