Compound Interest - Aptitude MCQ Questions and Solutions with Explanations

Simple Interest (I) = $$\frac{{PTR}}{{100}}$$
350 = $$\frac{{P \times 2 \times 4}}{{100}}$$
P = 4375

C.I = 175 + 175 + 7 = 357
Difference = 357 - 350 = Rs. 7

In one year there are 4 quarterly months.
∴ 9 month = 3 quarter
New Rate of Interest = $$\frac{8}{4}$$   = 2%
i.e 2% = $$\frac{1}{50}$$

Total CI = (100 + 100 + 100) + (2 + 2 +2) + 0.04
             = Rs.306.04

Let the sum of money be rs. P
Then,
$$\eqalign{ & \Rightarrow \left[ {P{{\left( {1 + \frac{R}{{100}}} \right)}^t} - P} \right] = {\text{C}}{\text{.I}}{\text{.}} \cr & \Rightarrow \left[ {P{{\left( {1 + \frac{{10}}{{100}}} \right)}^2} - P} \right] = 525 \cr & \Rightarrow P{\left( {\frac{{11}}{{10}}} \right)^2} - 1 = 525 \cr & \Rightarrow P\left( {\frac{{121}}{{100}} - 1} \right) = 525 \cr & \Rightarrow P\left( {\frac{{21}}{{100}}} \right) = 525 \cr & \Rightarrow P = \frac{{525 \times 100}}{{21}} \cr & \Rightarrow P = {\text{Rs}}{\text{.}}\,2500 \cr & \therefore {\text{ Sum of money}} \cr & {\text{ = Rs}}{\text{. 2500}} \cr} $$
Simple interest on the same sum Rs. 2500 for 4 (double the time) years at 5% (half the rate of percent per annum) is
So,
$$\eqalign{ & {\text{S}}{\text{.I}}{\text{. = Rs}}{\text{.}}\left( {\frac{{2500 \times 5 \times 4}}{{100}}} \right) \cr & \,\,\,\,\,\,\,\,\,{\text{ = Rs}}{\text{. 500}} \cr} $$

Let the sum be = 400x
Simple Interest = $$\frac{{PTR}}{{100}}$$
S.I = $$\frac{{400x \times 2 \times 5}}{{100}}$$ = 40x
for Compond Interest 5% = $$\frac{{1}}{20}$$

C.I = 20x + 20x + x = 41x
Difference = 41x - 40x = 20
i.e. x = 20
∴ Sum is = 400 × 20 = 8000

$$\eqalign{ & {\text{Rate}} = 10\% ,\, \cr & {\text{Let}}\,{\text{Principal}} = P \cr & {\text{S}}{\text{.I}}{\text{.}} = \frac{{P \times 10 \times 3}}{{100}} = \frac{{3P}}{{10}} \cr & {\text{C}}{\text{.I}}{\text{.}} = P\left\{ {{{\left( {1 + \frac{1}{{10}}} \right)}^3} - 1} \right\} \cr & \Rightarrow {\text{C}}{\text{.I}}{\text{.}}\,\, - \,\,{\text{S}}{\text{.I}}{\text{.}} = 992 \cr & \Rightarrow P\left\{ {{{\left( {1 + \frac{1}{{10}}} \right)}^3} - 1} \right\} - \frac{{3P}}{{10}} = 992 \cr & \Rightarrow P\left\{ {{{\left( {\frac{{11}}{{10}}} \right)}^3} - 1 - \frac{3}{{10}}} \right\} = 992 \cr & \Rightarrow P\left\{ {\frac{{\left( {1331 - 1000 - 300} \right)}}{{1000}}} \right\} = 992 \cr & \Rightarrow P\left( {\frac{{31}}{{1000}}} \right) = 992 \cr & \Rightarrow P = 32000 \cr} $$

Alternate:
Rate = 10% = $$\frac{1}{{10}}$$
Let principal ⇒ (10)³ = 1000
Interest 1^st year → 100
Interest 2^nd year → 100 + 10
Interest 3^rd year = 100 + 10 + 10 + 1
C.I – S.I = 331 – 300 = 31
31 → 992
1 → 32
P → 32000

$$\eqalign{ & \Rightarrow {\text{C}}{\text{.I}}{\text{.}} - {\text{S}}{\text{.I}}{\text{.}} = 41 \cr & \Rightarrow {\text{C}}{\text{.I}}{\text{.}} - {\text{S}}{\text{.I}}{\text{.}} = P{\left( {\frac{r}{{100}}} \right)^2} \cr & \Rightarrow 41 = P\left( {\frac{{25}}{{10000}}} \right) \cr & \Rightarrow P = 16400 \cr} $$

$$\eqalign{ & 10\% = \frac{1}{{10}} \cr & {\text{Let P}} = {\text{ }}{\left( {10} \right)^2} = 100 \cr & {\text{Total CI = 21 unit = 525}} \cr & {\text{1 unit = 25}} \cr & {\text{P}} = {\text{ 100 unit }} \cr & {\text{ = 100}} \times {\text{25}} = {\text{2500}} \cr & {\text{New Time = 4 years}} \cr & {\text{and new rate = 5}}\% \cr & {\text{SI = }}\frac{{2500 \times 4 \times 5}}{{100}}{\text{ }} \cr & {\text{SI = Rs. 500}} \cr} $$

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.
$$\therefore \frac{2}{3}{\text{of }}x \times \frac{{12 \times 6}}{{100}} = \frac{{48x}}{{100}}....(i)$$
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 we get
$$\eqalign{ & \Rightarrow \frac{{48x}}{{100}} + \frac{{7x}}{{100}} = 2750 \cr & \Rightarrow 55x = 2750 \times 100 \cr & \Rightarrow x = \frac{{2750 \times 100}}{{55}} \cr & \Rightarrow x = Rs.\,5000 \cr} $$

$$\eqalign{ & {\text{Rate of interest = 5}}\% {\text{ p}}{\text{.c}}{\text{.p}}{\text{.a}}{\text{.}} \cr & {\text{If time 3 years than CI}} - {\text{SI}} \cr & {\text{ = }}P\left[ {{{\left( {\frac{R}{{100}}} \right)}^3} + 3{{\left( {\frac{R}{{100}}} \right)}^2}} \right] \cr & \Rightarrow 122 = P\left[ {{{\left( {\frac{5}{{100}}} \right)}^3} + 3{{\left( {\frac{5}{{100}}} \right)}^2}} \right] \cr & \Rightarrow 122 = P\left( {\frac{{125}}{{1000000}} + \frac{{75}}{{10000}}} \right) \cr & \Rightarrow 122 = P\left[ {\frac{{125 + 7500}}{{1000000}}} \right] \cr & \Rightarrow 122 = P\left[ {\frac{{7525}}{{1000000}}} \right] \cr & \Rightarrow P = \frac{{122 \times 1000000}}{{7625}} \cr & \Rightarrow P = {\text{Rs}}{\text{. 16000}} \cr} $$

$$\eqalign{ & {\text{R}}\% {\text{ = }}\frac{{2662 - 2420}}{{2420}} \times 100 \cr & = \frac{{242}}{{2420}} \times 100 \cr & = 10\% \cr & {\text{2 years CI}}\% \cr & {\text{ = 10 + 10 + }}\frac{{10 \times 10}}{{100}} \cr & = 21\% \cr & {\text{So, 121}}\% {\text{ = 2420}} \cr & \Rightarrow {\text{100}}\% {\text{ = 2000}} \cr} $$