Interest - Study Mode

[#176] A sum fetched a total simple interest of Rs. 4016.25 at the rate of 9 p.c.p.a. in 5 years. What is the sum?
Correct Answer

(D) Rs. 8925

Explanation

Solution: $$eqalign{
& { ext{Principal}} cr
& = Rs.,left( {frac{{100 imes 4016.25}}{{9 imes 5}}}
ight) cr
& = Rs.,left( {frac{{401625}}{{45}}}
ight) cr
& = Rs.,8925 cr} $$

[#177] How much time will it take for an amount of Rs. 450 to yield Rs. 81 as interest at 4.5% per annum of simple interest?
Correct Answer

(B) 4 years

Explanation

Solution: $$eqalign{
& { ext{Time}} = left( {frac{{100 imes 81}}{{450 imes 4.5}}}
ight){ ext{years}} cr
& ,,,,,,,,,,,,,, = 4,{ ext{years}} cr} $$

[#178] Reena took a loan of Rs. 1200 with simple interest for as many years as the rate of interest. If she paid Rs. 432 as interest at the end of the loan period, what was the rate of interest?
Correct Answer

(B) 6

Explanation

Solution: $$eqalign{
& { ext{Let}},{ ext{rate}}, = R\% ,{ ext{and}} cr
& { ext{Time}},{ ext{ = }},{ ext{R}},{ ext{years}}{ ext{}} cr
& { ext{Then,}}, {frac{{1200 imes R imes R}}{{100}}} = 432 cr
& Rightarrow 12{R^2} = 432 cr
& Rightarrow {R^2} = 36 cr
& Rightarrow R = 6 cr} $$

[#179] A sum of Rs. 12,500 amounts to Rs. 15,500 in 4 years at the rate of simple interest. What is the rate of interest?
Correct Answer

(D) 6%

Explanation

Solution: $$eqalign{
& { ext{S}}{ ext{.I}}{ ext{.}} = Rs.,left( {15500 - 12500}
ight) cr
& ,,,,,,,,,, = Rs.,3000 cr
& { ext{Rate}} = left( {frac{{100 imes 3000}}{{12500 imes 4}}}
ight)\% cr
& ,,,,,,,,,,,,,, = 6\% cr} $$

[#180] An automobile financier claims to be lending money at simple interest, but he includes the interest every six months for calculating the principal. If he is charging an interest of 10%, the effective rate of interest becomes:
Correct Answer

(B) 10.25%

Explanation

Solution: $$eqalign{
& { ext{Let}},{ ext{the}},{ ext{sum}},{ ext{be}},{ ext{Rs}}{ ext{.}},{ ext{100}}{ ext{.}},{ ext{Then,}} cr
& { ext{S}}{ ext{.I}}{ ext{.}},{ ext{for}},{ ext{first}},{ ext{6}},{ ext{months}} cr
& = Rs.,left( {frac{{100 imes 10 imes 1}}{{100 imes 2}}}
ight) cr
& = Rs.,5 cr
& { ext{S}}{ ext{.I}}{ ext{.}},{ ext{for}},{ ext{last}},{ ext{6}},{ ext{months}} cr
& = Rs.,left( {frac{{105 imes 10 imes 1}}{{100 imes 2}}}
ight) cr
& = Rs.,5.25 cr} $$ So, amount at the end of 1 year = Rs. (100 + 5 + 5.25) = Rs. 110.25 ∴ Effective rate = (110.25 - 100) = 10.25%