Compound Interest - Study Mode

[#136] A sum of money becomes Rs. 11,880 after 4 years and Rs. 17,820 after 6 years on compound interest, if the interest is compounded annually. What is the half of the sum (in Rs.)?
Correct Answer

(B) 2,640

Explanation

Solution: $$eqalign{
& A = P{left( {1 + frac{R}{{100}}}
ight)^n} cr
& 11880 = P{left( {1 + frac{R}{{100}}}
ight)^4}.,.,.,.,.,left( { ext{i}}
ight) cr
& 17820 = P{left( {1 + frac{R}{{100}}}
ight)^6}.,.,.,.,.,left( {{ ext{ii}}}
ight) cr
& { ext{Equation }}left( {{ ext{ii}}}
ight){ ext{ divide by }}left( { ext{i}}
ight) cr
& frac{{17820}}{{11880}} = {left( {1 + frac{R}{{100}}}
ight)^2} cr
& frac{3}{2} = {left( {1 + frac{R}{{100}}}
ight)^2}.,.,.,.,.,{ ext{Put in equation}}left( { ext{i}}
ight) cr
& 11880 = P{left( {1 + frac{R}{{100}}}
ight)^4} cr
& 11880 = P{left( {1 + frac{R}{{100}}}
ight)^2}{left( {1 + frac{R}{{100}}}
ight)^2} cr
& 11880 = P imes frac{3}{2} imes frac{3}{2} cr
& P = 11880 imes frac{2}{3} imes frac{2}{3} cr
& P = 5280 cr
& { ext{Half part of sum}} = frac{1}{2} imes 5280 = 2640 cr} $$

[#137] Rs. 4,000 is given at 5% per annum for one year and interest is compounded half yearly. Rs. 2,000 is given at 40% per annum compounded quarterly for 1 year. The total interest received is nearest to:
Correct Answer

(C) Rs. 1,130.70

Explanation

Solution: $${x08f{Case - I}}$$ $$eqalign{
& = 100 + 100 + 2.5 = 202.5 cr
& {x08f{Case - II}} cr
& 2000 cr
& { ext{Rate of interest}} = frac{{40}}{4} = 10\% cr
& 2000 imes frac{{11}}{{10}} imes frac{{11}}{{10}} imes frac{{11}}{{10}} imes frac{{11}}{{10}} cr
& = frac{{14641}}{5} cr
& = 2928.2 cr
& { ext{Interest}} = 2928.2 - 2000 = 928.2 cr
& { ext{The total interest}} = 202.5 + 928.2 cr
& = 1130.7{ ext{ Answer}} cr} $$

[#138] What will be the compound interest on a sum of Rs. 31,250 for 2 years at 12% p.a., if the interest is compounded 8-monthly
Correct Answer

(D) Rs. 8,116

Explanation

Solution: $$eqalign{
& 12,{ ext{months}} o 12\% cr
& 8,{ ext{months}} o 8\% cr
& 8\% o frac{2}{{25}} cr} $$

[#139] A sum of money after a period of 2 years becomes Rs. 34,560, and it becomes Rs. 41,472 after a period of three years, being compounded at 'R' rate of interest. What is the value of R?
Correct Answer

(A) 20%

Explanation

Solution: $$eqalign{
& { ext{CI of 1 year}} = 41472 - 34560 = 6912 cr
& { ext{Rate }}\% = frac{{6912}}{{34560}} imes 100 cr
& = 2 imes 10 cr
& = 20\% { ext{ Answer}} cr} $$

[#140] In how many years will a sum of Rs. 320 amount to Rs. 405 if interest is compounded at 12.5% per annum?
Correct Answer

(A) 2 years

Explanation

Solution: [x08egin{array}{*{20}{c}}
{320}&:&{405} \
{sqrt {64} }&:&{sqrt {81} } \
8&:&9
end{array}] $$eqalign{
& 12frac{1}{2}\% o frac{1}{8} cr
& { ext{In one year}} = 8:9 cr
& { ext{Time}} = 2{ ext{ years}} cr} $$