Interest - Study Mode

[#6] At what rate of simple interest per annum can an amount of Rs. 1553.40 be obtained on the principal amount of Rs. 8630 after 3 years?
Correct Answer

4 p.c.p.a

Explanation

Solution: $$eqalign{
& { ext{P}} = { ext{Rs.}}{ ext{ 8630}} cr
& { ext{S}}{ ext{.I}}{ ext{.}} = { ext{Rs.}}{ ext{ 1553}}{ ext{.40}} cr
& { ext{T}} = { ext{3 years}} cr
& herefore { ext{Rate}} cr
& = left( {frac{{100 imes 1553.40}}{{8630 imes 3}}}
ight)\% cr
& = 6\% cr} $$

[#7] If simple interest on Rs. 600 for 4 years and on Rs. 600 for 2 years combined together is Rs.180, find the rate of interest.
Correct Answer

(B) 5%

Explanation

Solution: $$eqalign{
& { ext{Let the rate of be R}}\% { ext{p}}{ ext{.a}}{ ext{.}} cr
& Then, cr
& {frac{{600 imes R imes 4}}{{100}}} + {frac{{600 imes R imes 2}}{{100}}} = 180 cr
& Rightarrow 2400{ ext{R}} + 1200{ ext{R}} = 18000 cr
& Rightarrow 3600{ ext{R}} = 18000 cr
& Rightarrow { ext{R}} = 5\% cr} $$

[#8] A certain sum of money becomes three times of itself in 20 years at simple interest. In how many years does it become double itself at the same rate of simple interest ?
Correct Answer

(B) 10 years

Explanation

Solution: $$eqalign{
& { ext{Let principal = P}} cr
& herefore { ext{amount = 3P}} cr
& { ext{Interest = 3P}} - { ext{P}} cr
& ,,,,,,,,,,,,,,,,,,,,,{ ext{ = 2P}} cr
& { ext{According to the question,}} cr
& { ext{2P = }}frac{{{ ext{P}} imes { ext{R}} imes { ext{20}}}}{{100}} cr
& Rightarrow { ext{R = 10% }} cr} $$ Let after t years it will become double $$eqalign{
& { ext{Hence,}} cr
& { ext{Interest = 2P}} - { ext{P = P}} cr
& Rightarrow { ext{P = }}frac{{{ ext{P}} imes 10 imes { ext{t}}}}{{100}} cr
& Rightarrow { ext{t = 10 years}} cr} $$

[#9] A person borrows some money for 5 years and ratio of loan amount : total interest amount is 5 : 2. Then find the ratio of loan amount : interest rate is equal to = ?
Correct Answer

(D) 25 : 2

Explanation

Solution: $$eqalign{
& { ext{Loan Amount}}:{ ext{Total Interest}} cr
& { ext{5}}:{ ext{2}} cr
& { ext{Principal}} o { ext{5}} cr
& { ext{Interest for 1 year}} Rightarrow { ext{2}} cr
& { ext{Interest for 5 year}} Rightarrow { ext{10}} cr
& { ext{10}} = frac{{5 imes { ext{R}} imes 5}}{{100}} cr
& { ext{R}}\% = 40\% cr
& = frac{{40}}{{100}} = frac{2}{5} cr
& { ext{P}}:{ ext{R}} = 5:frac{2}{5} cr
& ,,,,,,,,,,,,,, = 25:2 cr} $$

[#10] 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: $$eqalign{
& { ext{Half yearly rate}} cr
& { ext{ = }}frac{6}{2} = 3\% cr
& { ext{Effective rate % }} cr
& { ext{ = 3}} + { ext{3}} + frac{{3 imes 3}}{{100}} cr
& = 6.09\% cr} $$