Compound Interest - Aptitude MCQ Questions and Solutions with Explanations

Interest for 2 years at the rate of 15%
$$\eqalign{ & {\text{ = 15 + 15 + }}\frac{{15 \times 15}}{{100}} \cr & = 32.25\% \cr & {\text{According to question,}} \cr & {\text{32}}{\text{.25}}\% {\text{ = 3225}} \cr & {\text{100}}\% {\text{ = }}\frac{{3225}}{{32.25}} \times 100 \cr & = 100 \times 100 = 10000 \cr} $$

$$\eqalign{ & {\text{10}}\% {\text{ = }}\frac{1}{{10}} \cr & {\text{Principal}}\,\,\,\,\,\,\,{\text{Amount}} \cr & \,\,\,\,\,\,\,{\text{10}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,11 \cr & \,\,\,\,\,\,\,{\text{10}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,11 \cr & \,\,\,\,\,\,\,{\text{10}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,11 \cr & \,\,\,\,\,\,\,{\text{10}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,11 \cr & \underbrace {\overline {\,\,\,10000\,\,\,\,\,\,{\text{:}}\,\,\,\,\,{\text{14641}}\,\,\,} }_{{\text{CI = 4641}}} \cr & \because {\text{Principal = 10000 units}} \cr & {\text{ = Rs}}{\text{. 4000 (given)}} \cr & {\text{1 unit = }}\frac{2}{5} \cr & {\text{CI = 4641 unit}} \cr & {\text{ = Rs}}{\text{. }}\left( {\frac{2}{5} \times 4641} \right) \cr & = {\text{Rs}}{\text{. }}1856.40 \cr} $$

10% = $$\frac{1}{{10}}$$
\[\begin{array}{*{20}{c}} {}&{{\text{Principal}}\,\,\,\,\,\,\,\,\,{\text{Interest}}} \\ {{\text{I}} \to }&{{{10}_{ \times 11 = 110}}\,\,\,\,\,{{11}_{ \times 11 = 121}}} \\ {{\text{II}} \to }&{{{10}^2}_{ = 100}\,\,\,\,\,\,\,\,\,\,{{11}^2}_{ = 121}} \\ {{\text{Total}} \to }&{\overline {\underline {\,210\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,242\,\,\,} } } \end{array}\]
Total interest on sum = 242 - 210 = 32 units
121 units → 5808
1 unit → 48
32 units → 48 × 32 = 1536
Total interest of 60% = 1536 × $$\frac{{60}}{{100}}$$
= Rs. 921.6 ∼ Rs. 922

$$\eqalign{ & 8\% = \frac{{ + 2}}{{25}},\,35\% = \frac{{ - 7}}{{20}},\,65\% = \frac{{ + 13}}{{20}} \cr & 8000000 \times \frac{{27}}{{25}} \times \frac{{13}}{{20}} \times \frac{{33}}{{20}} \cr & = 800 \times 27 \times 13 \times 33 \cr & = 9266400{\text{ Answer}} \cr} $$

$$\eqalign{ & {\text{Rate}} = 10\% = \frac{1}{{10}} \cr & {\text{Time}} = 5\,{\text{years}} \cr} $$

$$\eqalign{ & 4630.50 = 4000{\left( {1 + \frac{R}{{100}}} \right)^3} \cr & 9261 = 8000{\left( {1 + \frac{R}{{100}}} \right)^3} \cr & \frac{{9261}}{{8000}} = {\left( {1 + \frac{R}{{100}}} \right)^3} \cr & {\left( {\frac{{21}}{{20}}} \right)^3} = {\left( {1 + \frac{R}{{100}}} \right)^3} \cr & \frac{{21}}{{20}} = \left( {1 + \frac{R}{{100}}} \right) \cr & \frac{1}{{20}} = \frac{R}{{100}} \cr & R = 5 \cr} $$

$$\eqalign{ & 15000\left[ {{{\left( {1 + \frac{{20}}{{100}}} \right)}^3} - 1} \right] + 20000\left[ {{{\left( {1 + \frac{{30}}{{100}}} \right)}^3} - 1} \right] \cr & = 15000\left( {\frac{{216}}{{125}} - 1} \right) + 20000\left( {\frac{{2197}}{{1000}} - 1} \right) \cr & = 15000 \times \frac{{91}}{{125}} + 20000 \times \frac{{1197}}{{1000}} \cr & = 10920 + 23940 \cr & = {\text{Rs}}{\text{. }}34860 \cr} $$

R = 10%, T = 2 year, SI = Rs. 8100
$$8100 = \frac{{{\text{P}} \times 10 \times 2}}{{100}}$$
40500 = P
Now same principal
R% = 15%
T = 2 year
CI = ?
$$15\% = \frac{3}{{20}}$$

$${\text{CI}} = \frac{{129 \times 405}}{4} = 13061.25$$

$$\eqalign{ & {\text{P}} \times \frac{{27,900}}{{18,600}} = 18,600 \cr & {\text{P}} = \frac{{18,600 \times 186}}{{279}} \cr & {\text{P}} = 12,400 \cr} $$