Compound Interest - Study Mode

[#106] What will be the compound interest on a sum of Rs. 25,000 after 3 years at the rate of 12 p.c.p.a.?
Correct Answer

(C) Rs. 10123.20

Explanation

Solution: $$eqalign{
& { ext{Amount}} = Rs.,left[ {25000 imes {{left( {1 + frac{{12}}{{100}}}
ight)}^3}}
ight] cr
& ,,,,,,,,,,,,,,,,,,,,,,,, = Rs.,left( {25000 imes frac{{28}}{{25}} imes frac{{28}}{{25}} imes frac{{28}}{{25}}}
ight) cr
& ,,,,,,,,,,,,,,,,,,,,,,,, = Rs.,35123.20 cr
& herefore { ext{C}}{ ext{.I}}{ ext{.}} = Rs.left( {35123.20 - 25000}
ight) cr
& ,,,,,,,,,,,,,,,,,, = Rs.,10123.20 cr} $$

[#107] At what rate of compound interest per annum will a sum of Rs. 1200 become Rs. 1348.32 in 2 years?
Correct Answer

(A) 6%

Explanation

Solution: $$eqalign{
& { ext{Let}},{ ext{the}},{ ext{rate}},{ ext{be}},R\% ,p.a. cr
& { ext{Then}},,1200 imes {left( {1 + frac{R}{{100}}}
ight)^2} = 1348.32 cr
& Rightarrow {left( {1 + frac{R}{{100}}}
ight)^2} = frac{{134832}}{{120000}} = frac{{11236}}{{10000}} cr
& herefore {left( {1 + frac{R}{{100}}}
ight)^2} = {left( {frac{{106}}{{100}}}
ight)^2} cr
& Rightarrow 1 + frac{R}{{100}} = frac{{106}}{{100}} cr
& Rightarrow R = 6\% cr} $$

[#108] The least number of complete years in which a sum of money put out at 20% compound interest will be more than doubled is:
Correct Answer

(B) 4

Explanation

Solution: $$eqalign{
& P{left( {1 + frac{{20}}{{100}}}
ight)^n} > 2P,,, Rightarrow ,,,{left( {frac{6}{5}}
ight)^n} > 2 cr
& { ext{Now}},left( {frac{6}{5} imes frac{6}{5} imes frac{6}{5} imes frac{6}{5}}
ight) > 2 cr
& So,,n = 4,{ ext{years}} cr} $$

[#109] Albert invested an amount of Rs. 8000 in a fixed deposit scheme for 2 years at compound interest rate 5 p.c.p.a. How much amount will Albert get on maturity of the fixed deposit?
Correct Answer

(C) Rs. 8820

Explanation

Solution: $$eqalign{
& { ext{Amount}} = Rs.left[ {8000 imes {{left( {1 + frac{5}{{100}}}
ight)}^2}}
ight] cr
& ,,,,,,,,,,,,,,,,,,,,,,, = Rs.,left( {8000 imes frac{{21}}{{20}} imes frac{{21}}{{20}}}
ight) cr
& ,,,,,,,,,,,,,,,,,,,,,,, = Rs.,8820 cr} $$

[#110] The effective annual rate of interest corresponding to a nominal rate of 6% per annum payable half-yearly is:
Correct Answer

(D) 6.09%

Explanation

Solution: $$eqalign{
& { ext{Amount}},{ ext{of}},{ ext{Rs}}{ ext{.}},{ ext{100}},{ ext{for}},{ ext{1}},{ ext{year}},{ ext{when}}, cr
& { ext{compounded}},{ ext{half - yearly}} cr
& = Rs.,left[ {100 imes {{left( {1 + frac{3}{{100}}}
ight)}^2}}
ight] cr
& = Rs.,106.09 cr
& herefore { ext{Effective}},{ ext{rate}} = left( {106.09 - 100}
ight)\% cr
& = 6.09\% cr} $$