Interest - Aptitude MCQ Questions and Solutions with Explanations

$$\eqalign{ & {\text{P = Principal}}\,{\text{Amount}} \cr & {\text{T = }}\,{\text{Time}}\,{\text{period}} \cr & {\text{R = Rate}}\,{\text{of}}\,{\text{Interest}} \cr & I = \frac{{P \times T \times R}}{{100}} \cr & I = \frac{{5200 \times 2 \times 6}}{{100}} \cr & I = 624. \cr} $$

$$\eqalign{ & A = P + I \cr & A = 1200 + {\frac{{PTR}}{{100}}} \cr & A = {1200 + {\frac{{1200 \times 5 \times 3}}{{100}}} } \cr & {\text{Amount}},\,A = Rs.\,1380 \cr} $$

$$\eqalign{ & {\text{Let rate is }}R\% \cr & {\text{We have}}, \cr & I = \frac{{PTR}}{{100}} \cr & {\text{Here}},1500 = \frac{{5000 \times 3 \times R}}{{100}} \cr & {\text{Thus}},R = 10\% \cr} $$

$$\eqalign{ & {\text{We}}\,{\text{can}}\,{\text{use}}\,{\text{formula}}\,{\text{of}}\,{\text{compound}}\,{\text{interest}} \cr & A = P \times {\left[ {1 + \left( {\frac{r}{{100}}} \right)} \right]^n} \cr & A = 2100 \times {\left[ {1 + \left( {\frac{5}{{100}}} \right)} \right]^2} \cr & A = 2100 \times {\left[ {\frac{{105}}{{100}}} \right]^2} \cr & A = \frac{{ {2100 \times 11025} }}{{10000}} \cr & {\text{Hence,}}\,{\text{Amount}}\,A = Rs.\,2315.25 \cr} $$

$$\eqalign{ & {\text{The}}\,{\text{difference}}\,{\text{between}}\,{\text{compound}}\,{\text{interest}}\,{\text{and}} \cr & {\text{simple}}\,{\text{interest}}\,{\text{over}}\,{\text{two}}\,{\text{years}}\,{\text{is}}\,{\text{given}}\,{\text{by}} \cr & \frac{{{{\Pr }^2}}}{{{{100}^2}}}\,or\,P{\left( {\frac{r}{{100}}} \right)^2} \cr & {\text{Here,}}\,{\text{Principal}}\,\left( P \right) = Rs.\,2000 \cr & {\text{Rate}}\,\left( r \right) = 5\% \cr & {\text{Now}}\,{\text{difference}}, \cr & D = \frac{{ {2000 \times 5 \times 5} }}{{ {100 \times 100} }} \cr & D = Rs.\,5 \cr} $$

$$\eqalign{ & {\text{Amount}},\,A = Rs.\,1440 \cr & {\text{Principal}},\,P = Rs.\,1200 \cr & {\text{Interest}},\,I = Rs.\,\left( {1440 - 1200} \right) = 240 \cr & R = \frac{{ {240 \times 100} }}{{ {1200 \times 2} }} = 10\% \cr & \cr & {\text{Alternatively}}, \cr & {\text{We}}\,{\text{can}}\,{\text{go}}\,{\text{through}}\,{\text{a}}\,{\text{thought}}\,{\text{process}}\,i.e. \cr & 1200\, == 20\% \uparrow \left( {240\,{\text{in}}\,2\,{\text{years}}} \right) ⇒ 1400 \cr & {\text{That}}\,{\text{means}}\,10\% \,{\text{rise}}\,{\text{in}}\,{\text{each}}\,{\text{year}} \cr} $$

$$\eqalign{ & {I_1} = \frac{{P{T_1}{R_1}}}{{100}} \cr & {I_1} = \frac{{ {500 \times 3 \times 5} }}{{100}} \cr & \,\,\,\,\,\,\, = Rs.{\kern 1pt} 75 \cr & {I_2} = \frac{{P{T_2}{R_2}}}{{100}} \cr & {I_2} = \frac{{ {500 \times 4 \times 4} }}{{100}} \cr & \,\,\,\,\,\,\,\, = Rs.{\kern 1pt} 80 \cr & {\text{Difference}} = 80 - 75 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\,5 \cr} $$

Alternatively
The interest is calculated simply and then it will have a rise of 15% in 1^st case and 16% in 2^nd case.
Difference = 1% on 500 = Rs. 5

Otherway,
500 == 15% $$ \uparrow $$ ⇒ 575 (1^st case)
500 == 16% $$ \uparrow $$ ⇒ 580 (2^nd case)
We can see clear difference of Rs. 5

$$\eqalign{ & {1^{{\text{st}}}}{\kern 1pt} {\text{case}}: \cr & {I_1} = \frac{{700 \times 3 \times 8}}{{100}} = {\text{Rs}}{\text{. }}168 \cr & {2^{{\text{nd}}}}{\kern 1pt} {\text{case}}: \cr & {I_2} = \frac{{700 \times 2 \times 7.5}}{{100}} = {\text{Rs}}{\text{. }}105 \cr} $$
Then total interest for five years
$$ = \left( {{I_1} + {I_2}} \right) = {\text{Rs}}{\text{. }}273$$

Alternatively,
As interest is calculated as simple interest
So, we can add up rates for all given 5 years and calculate it easily i.e.
For the five years rate
= (8 × 3 + 7.5 × 2)
= 39%
Now,
700 = 39% $$ \uparrow $$ ⇒ 973
Interest = Rs. 273
The thought can go this way we internally calculated
$$\eqalign{ & {\kern 1pt} 10\% \,{\text{of}}\,700 = {\frac{{700}}{{10}}} = 70 \cr & {\text{Then}}, \cr & 39\% \,{\text{of}}\,700 \cr & = \left( {40\% - 1\% } \right)\,{\text{of}}\,700 \cr & = \left( {280 - 7} \right) \cr & = 273 \cr} $$

$$\eqalign{ & {\text{Given,}}\,{\text{Principal}},\,P = Rs.\,1000 \cr & {\text{Compoind}}\,{\text{rate}},\,R = 20\% \,{\text{per}}\,{\text{annum}} \cr & = \frac{{20}}{2} = 10\% \,{\text{half - yearly}} \cr & {\text{Time}} = 18\,{\text{month}} = 3\,{\text{half - years}} \cr & {\text{Amount}}, \cr & A = \left\{ {P \times {{\left[ {1 + \left( {\frac{R}{{100}}} \right)} \right]}^n}} \right\} \cr & = \left\{ {1000 \times {{\left[ {1 + \left( {\frac{{10}}{{100}}} \right)} \right]}^3}} \right\} \cr & = { {\frac{{1000 \times 11 \times 11 \times 11}}{{10 \times 10 \times 10}}} } \cr & A = Rs.\,1331 \cr & {\text{Hence,}}\,{\text{compound}}\,{\text{interest}} = Rs.\,331 \cr} $$

$$\eqalign{ & {\text{Given}}, \cr & {\text{Compound}}\,{\text{rate}},\,R = 10\% \,{\text{per}}\,{\text{annum}} \cr & {\text{Time}} = 2\,{\text{years}} \cr & CI - Rs.\,420 \cr & {\text{Let}}\,P\,{\text{be}}\,{\text{the}}\,{\text{required}}\,{\text{principal}} \cr & A = \left( {P + CI} \right) \cr & {\text{Amount}},A = \left\{ {P \times {{\left[ {1 + \left( {\frac{R}{{100}}} \right)} \right]}^n}} \right\} \cr & \left( {P + CI} \right) = \left\{ {P \times {{\left[ {1 + \frac{{10}}{{100}}} \right]}^2}} \right\} \cr & \left( {P + 420} \right) = P \times {\left[ {\frac{{11}}{{10}}} \right]^2} \cr & P - 1.21P = - 420 \cr & 0.21P = 420 \cr & {\text{Hence}},P = \frac{{420}}{{0.21}} = Rs.\,2000 \cr} $$