Compound Interest - Study Mode

[#141] A sum of Rs. 4,620 is to be paid back in 2 equal annual instalments. How much is each instalments (in Rs.) if the interest is compounded annually at 10% per annum?
Correct Answer

(C) 2,662

Explanation

Solution: $$eqalign{
& P = { ext{Rs}}{ ext{. }}4620 cr
& R = 10\% = frac{1}{{10}} cr} $$ [x08egin{array}{*{20}{c}}
{{ ext{Principal}}}&{{ ext{Instalments}}} \
{110 = 10 imes 11}&{11 imes 11 = 121} \
{100 = 100}&{121} \
x08egin{gathered}
210 hfill \
,,,,,{ downarrow ^{ imes 22}} hfill \
end{gathered} &x08egin{gathered}
hfill \
,,,,,{ downarrow ^{ imes 22}} hfill \
end{gathered} \
{4620}&{{ ext{Rs}}{ ext{. }}{mathbf{2662}}}
end{array}]

[#142] A sum of Rs. 18,000 is lent at 10% p.a. compound interest, compounded annually. What is the difference between the compound interest for 3 rd year and 4 th year?
Correct Answer

(B) Rs. 217.80

Explanation

Solution: Difference of compound interest = 131 - 10 = 121 10000 → 18000 1 → 1.8 121 → 121 × 1.8 = 217.8

[#143] A loan is to be returned in two equal yearly instalments. If the rate of interest is 10% p.a., compounded annually, and each instalment if Rs. 5,808, then the total interest charged in this scheme is:
Correct Answer

(B) Rs. 1,536

Explanation

Solution: $$eqalign{
& 5808 imes frac{{10}}{{11}} imes frac{{21}}{{11}} cr
& { ext{Principal}} = 10080 cr
& { ext{Amount}} = 5808 imes 2 = 11616 cr
& { ext{Interest}} = 1536 cr} $$

[#144] What is the amount (in Rs.) of a sum of Rs. 32,000 at 20% per annum for 9 months, compounded quarterly?
Correct Answer

(A) 37,044

Explanation

Solution: $$eqalign{
& { ext{Principal}} = { ext{Rs}}{ ext{. }}32000 cr
& { ext{Rate}} = 20\% { ext{ p}}{ ext{.a}}{ ext{.}} cr
& = frac{{20}}{4}\% = 5\% { ext{ quarterly}} = frac{1}{{20}} cr
& { ext{Time}} = 9{ ext{ months}} = frac{9}{{12}} imes 4 = 3 cr} $$ [x08egin{array}{*{20}{c}}
{{ ext{Principal}}}&{}&{{ ext{Amount}}} \
{{{left( {20}
ight)}^3}}&:&{{{left( {21}
ight)}^3}} \
{8000}&:&{9261} \
{,,,,,{ downarrow ^{ imes 4}}}&{}&{,,,,,{ downarrow ^{ imes 4}}} \
{{ ext{Rs}}{ ext{. }}32000}&{}&{x08oxed{{ ext{Rs}}{ ext{. }}37044}}
end{array}]

[#145] The compound interest on a sum of Rs. 5,500 at 15% p.a. for 2 years, when the interest is compounded 8 monthly is:
Correct Answer

(C) Rs. 1,820.50

Explanation

Solution: 12 months ⟶ 15% 8 months ⟶ 10% 1000 units ⟶ 5500 1 unit ⟶ 5.5 331 units ⟶ 331 × 5.5 = Rs. 1820.50