Interest - Study Mode
[#56] Find the rate of interest if the amount after 2 years of simple interest on a capital of Rs. 1200 is Rs. 1440.
Correct Answer
(C) 10%
Explanation
Solution: $$eqalign{
& { ext{Amount}},,A = Rs.,1440 cr
& { ext{Principal}},,P = Rs.,1200 cr
& { ext{Interest}},,I = Rs.,left( {1440 - 1200}
ight) = 240 cr
& R = frac{{ {240 imes 100} }}{{ {1200 imes 2} }} = 10\% cr
& cr
& { ext{Alternatively}}, cr
& { ext{We}},{ ext{can}},{ ext{go}},{ ext{through}},{ ext{a}},{ ext{thought}},{ ext{process}},i.e. cr
& 1200, == 20\% uparrow left( {240,{ ext{in}},2,{ ext{years}}}
ight) ⇒ 1400 cr
& { ext{That}},{ ext{means}},10\% ,{ ext{rise}},{ ext{in}},{ ext{each}},{ ext{year}} cr} $$
[#57] What is the difference between the simple interest on a principal of Rs. 500 being calculated at 5% per annum for 3 years and 4% per annum for 4 years?
Correct Answer
(A) Rs. 5
Explanation
Solution: $$eqalign{
& {I_1} = frac{{P{T_1}{R_1}}}{{100}} cr
& {I_1} = frac{{ {500 imes 3 imes 5} }}{{100}} cr
& ,,,,,,, = Rs.{kern 1pt} 75 cr
& {I_2} = frac{{P{T_2}{R_2}}}{{100}} cr
& {I_2} = frac{{ {500 imes 4 imes 4} }}{{100}} cr
& ,,,,,,,, = Rs.{kern 1pt} 80 cr
& { ext{Difference}} = 80 - 75 cr
& ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, = { ext{Rs}}{ ext{.}},5 cr} $$ 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
[#58] What is the simple interest on a sum of Rs. 700 if the rate of interest for the first 3 years is 8% per annum and for the last 2 years is 7.5% per annum?
Correct Answer
(C) Rs. 273
Explanation
Solution: $$eqalign{
& {1^{{ ext{st}}}}{kern 1pt} { ext{case}}: cr
& {I_1} = frac{{700 imes 3 imes 8}}{{100}} = { ext{Rs}}{ ext{. }}168 cr
& {2^{{ ext{nd}}}}{kern 1pt} { ext{case}}: cr
& {I_2} = frac{{700 imes 2 imes 7.5}}{{100}} = { ext{Rs}}{ ext{. }}105 cr} $$ Then total interest for five years $$ = left( {{I_1} + {I_2}}
ight) = { ext{Rs}}{ ext{. }}273$$ 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 $$eqalign{
& {kern 1pt} 10\% ,{ ext{of}},700 = {frac{{700}}{{10}}} = 70 cr
& { ext{Then}}, cr
& 39\% ,{ ext{of}},700 cr
& = left( {40\% - 1\% }
ight),{ ext{of}},700 cr
& = left( {280 - 7}
ight) cr
& = 273 cr} $$
[#59] Find the compound interest on Rs. 1000 at the rate of 20% per annum for 18 month when interest is compounded half yearly.
Correct Answer
(A) Rs. 331
Explanation
Solution: $$eqalign{
& { ext{Given,}},{ ext{Principal}},,P = Rs.,1000 cr
& { ext{Compoind}},{ ext{rate}},,R = 20\% ,{ ext{per}},{ ext{annum}} cr
& = frac{{20}}{2} = 10\% ,{ ext{half - yearly}} cr
& { ext{Time}} = 18,{ ext{month}} = 3,{ ext{half - years}} cr
& { ext{Amount}}, cr
& A = left{ {P imes {{left[ {1 + left( {frac{R}{{100}}}
ight)}
ight]}^n}}
ight} cr
& = left{ {1000 imes {{left[ {1 + left( {frac{{10}}{{100}}}
ight)}
ight]}^3}}
ight} cr
& = { {frac{{1000 imes 11 imes 11 imes 11}}{{10 imes 10 imes 10}}} } cr
& A = Rs.,1331 cr
& { ext{Hence,}},{ ext{compound}},{ ext{interest}} = Rs.,331 cr} $$
[#60] Find the principal if the interest compounded at the rate of 10% per annum for two years is Rs. 420.
Correct Answer
(C) Rs. 2000
Explanation
Solution: $$eqalign{
& { ext{Given}}, cr
& { ext{Compound}},{ ext{rate}},,R = 10\% ,{ ext{per}},{ ext{annum}} cr
& { ext{Time}} = 2,{ ext{years}} cr
& CI - Rs.,420 cr
& { ext{Let}},P,{ ext{be}},{ ext{the}},{ ext{required}},{ ext{principal}} cr
& A = left( {P + CI}
ight) cr
& { ext{Amount}},A = left{ {P imes {{left[ {1 + left( {frac{R}{{100}}}
ight)}
ight]}^n}}
ight} cr
& left( {P + CI}
ight) = left{ {P imes {{left[ {1 + frac{{10}}{{100}}}
ight]}^2}}
ight} cr
& left( {P + 420}
ight) = P imes {left[ {frac{{11}}{{10}}}
ight]^2} cr
& P - 1.21P = - 420 cr
& 0.21P = 420 cr
& { ext{Hence}},P = frac{{420}}{{0.21}} = Rs.,2000 cr} $$