1. The difference between compound interest and simple interest on a certain sum of money for 2 years at 5% per annum is Rs. 41. What is the sum of money ?
a) Rs. 7200
b) Rs. 9600
c) Rs. 16400
d) Rs. 8400
Explanation:
$$\eqalign{ & {\text{C}}{\text{.I}}{\text{.}} - {\text{S}}{\text{.I}}{\text{.}} = 41 \cr & {\text{C}}{\text{.I}}{\text{.}} - {\text{S}}{\text{.I}}{\text{.}} = P{\left( {\frac{r}{{100}}} \right)^2} \cr & 41 = P\left( {\frac{{25}}{{10000}}} \right) \cr & P = 16400 \cr} $$
2. The compound interest on a certain sum for 2 years at 10% per annum is Rs. 525. The simple interest on the same sum for double the time at half the rate percent per annum is = ?
a) Rs. 520
b) Rs. 550
c) Rs. 500
d) Rs. 515
Explanation:
$$\eqalign{ & 10\% = \frac{1}{{10}} \cr & {\text{Let P}} = {\text{ }}{\left( {10} \right)^2} = 100 \cr & {\text{Total CI = 21 unit = 525}} \cr & {\text{1 unit = 25}} \cr & {\text{P}} = {\text{ 100 unit }} \cr & {\text{ = 100}} \times {\text{25}} = {\text{2500}} \cr & {\text{New Time = 4 years}} \cr & {\text{and new rate = 5}}\% \cr & {\text{SI = }}\frac{{2500 \times 4 \times 5}}{{100}}{\text{ }} \cr & {\text{SI = Rs. 500}} \cr} $$
3. Shashi had a certain amount of money. He invested $$\frac{2}{3}$$ of the total money in scheme A for 6 years and rest of the money he invested in scheme B for 2 years. Scheme A offers simple interest at a rate of 12% p.a. and scheme B offers compound interest ( compound annually) at a rate of 10% p.a. If the total interest obtained from both the schemes is Rs. 2750. What was the total amount invested by him in scheme A and scheme B together ? (Approximate value)
a) Rs. 4500
b) Rs. 4200
c) Rs. 4050
d) Rs. 5000
Explanation: Let the total sum of money invested by Shashi be Rs. x
In scheme A money invested at simple interest for 6 years at a rate of 12% p.a.
$$ \frac{2}{3}{\text{of }}x \times \frac{{12 \times 6}}{{100}} = \frac{{48x}}{{100}}....(i)$$
In scheme B money at compound interest for 2 year at a rate of 10% p.a.
$$\eqalign{ & \frac{x}{3}{\left( {1 + \frac{{10}}{{100}}} \right)^2} - \frac{x}{3} \cr & \Rightarrow \frac{x}{3}{\left( {1 + \frac{{10}}{{100}}} \right)^2} - \frac{x}{3} = \frac{{7x}}{{100}} \cr} $$
According to given information,
$$\eqalign{ & \frac{{48x}}{{100}} + \frac{{7x}}{{100}} = 2750 \cr & 55x = 2750 \times 100 \cr & x = \frac{{2750 \times 100}}{{55}} \cr & x = Rs.\,5000 \cr} $$
4. The difference between CI and SI on a certain sum of money for 3 years at 5% p.a. is Rs. 122. Find the sum invested ?
a) Rs. 10000
b) Rs. 12000
c) Rs. 16000
d) Rs. 20000
Explanation:
$$\eqalign{ & {\text{Rate of interest = 5}}\% {\text{ p}}{\text{.c}}{\text{.p}}{\text{.a}}{\text{.}} \cr & {\text{If time 3 years than CI}} - {\text{SI}} \cr & {\text{ = }}P\left[ {{{\left( {\frac{R}{{100}}} \right)}^3} + 3{{\left( {\frac{R}{{100}}} \right)}^2}} \right] \cr & \Rightarrow 122 = P\left[ {{{\left( {\frac{5}{{100}}} \right)}^3} + 3{{\left( {\frac{5}{{100}}} \right)}^2}} \right] \cr & \Rightarrow 122 = P\left( {\frac{{125}}{{1000000}} + \frac{{75}}{{10000}}} \right) \cr & 122 = P\left[ {\frac{{125 + 7500}}{{1000000}}} \right] \cr & 122 = P\left[ {\frac{{7525}}{{1000000}}} \right] \cr & P = \frac{{122 \times 1000000}}{{7625}} \cr & P = {\text{Rs}}{\text{. 16000}} \cr} $$
5. A man invested a sum of money at compound interest. It amounted to Rs. 2420 in 2 years and to Rs. 2662 in 3 years. Find the sum ?
a) Rs. 1000
b) Rs. 2000
c) Rs. 5082
d) Rs. 3000
Explanation:
$$\eqalign{ & {\text{R}}\% {\text{ = }}\frac{{2662 - 2420}}{{2420}} \times 100 \cr & = \frac{{242}}{{2420}} \times 100 \cr & = 10\% \cr & {\text{2 years CI}}\% \cr & {\text{ = 10 + 10 + }}\frac{{10 \times 10}}{{100}} \cr & = 21\% \cr & {\text{So, 121}}\% {\text{ = 2420}} \cr & \Rightarrow {\text{100}}\% {\text{ = 2000}} \cr} $$
6. A sum of Rs. 8000 will amount to Rs. 8820 in 2 years if the interest is calculated every year. The rate of compound interest is = ?
a) 6%
b) 7%
c) 3%
d) 5%
Explanation:
$$\eqalign{ & {\text{Principal = Rs 8000}} \cr & {\text{Amount = Rs 8820}} \cr & {\text{Let Rate = }}R \cr & {\text{Time = 2 years}} \cr & {\text{By using formula, }} \cr & 8820 = 8000{\left( {1 + \frac{R}{{100}}} \right)^2} \cr & \frac{{8820}}{{8000}} = {\left( {1 + \frac{R}{{100}}} \right)^2} \cr & \frac{{441}}{{400}} = {\left( {1 + \frac{R}{{100}}} \right)^2} \cr & {\text{Taking square root of both sides,}} \cr & \frac{{21}}{{20}} = \left( {1 + \frac{R}{{100}}} \right) \cr & R = 5\% \cr} $$
7. The compound interest on a certain some of money for 2 years at 10% per annum is Rs 420. The simple interest on the same sum at the same rate and for the same time will be ?
a) Rs. 350
b) Rs. 375
c) Rs. 380
d) Rs. 400
Explanation:
$$\eqalign{ & {\text{Rate = 10}}\% \cr & {\text{Time = 2 years}} \cr & {\text{Effective rate of CI for 2 years}} \cr & {\text{ = 10 + 10 + }}\frac{{10 \times 10}}{{100}} = 21\% \cr & {\text{Effective rate of SI for 2 years}} \cr & {\text{ = 2}} \times {\text{10 = 20}}\% \cr & {\text{Required SI}} \cr & {\text{ = }}\frac{{420}}{{21}} \times {\text{20 = Rs. 400}} \cr} $$
8. A sum of money at compound interest amounts to thrice of itself in 3 years. In how many years it will be 9 times of itself ?
a) 9 years
b) 27 years
c) 6 years
d) 3 years
Explanation: x becomes 3x in 3 years
Therefore 3x also becomes 9x in 3 years
Required years = 3 + 3 = 6
9. A father left a will of Rs. 16400 for his two sons aged 17 and 18 years. They must get equal amount when they are 20 years, at 5% compound interest. Find the present share of the younger son = ?
a) Rs. 8000
b) Rs. 8200
c) Rs. 8400
d) Rs. 8800
Explanation:
Let the share of the younger and elder sons be Rs. x and Rs. (16400 - x)
Then, amount of Rs. x after 3 years = Amount of Rs. (16400 - x) after 2 years
$$\eqalign{ & x{\left( {1 + \frac{5}{{100}}} \right)^3} = \left( {16400 - x} \right){\left( {1 + \frac{5}{{100}}} \right)^2} \cr & x\left( {1 + \frac{5}{{100}}} \right) = \left( {16400 - x} \right) \cr & \frac{{21x}}{{20}} + x = 16400 \cr & \frac{{41x}}{{20}} = 16400 \cr & x = \left( {\frac{{16400 \times 20}}{{41}}} \right) \cr & x = 8000 \cr} $$
10. A sum of money put at compound interest amounts in 2 years to Rs. 672 and in 3 years Rs. 714. The rate of interest per annum is = ?
a) 5.5%
b) 6.0%
c) 6.25%
d) 6.75%
Explanation:
$$\eqalign{ & {\text{S}}{\text{.I}}{\text{. on Rs}}{\text{. 672 for 1 year}} \cr & {\text{ = Rs}}{\text{. }}\left( {714 - 672} \right) \cr & {\text{ = Rs}}{\text{. 42}} \cr & {\text{Rate = }}\left( {\frac{{100 \times 42}}{{672 \times 1}}} \right){\text{% }} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{ = 6}}{\text{.25% }} \cr} $$