Interest - Study Mode

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

[#117] A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4 years. The sum is
Correct Answer

(C) Rs. 698

Explanation

Solution: $$eqalign{
& { ext{S}}{ ext{.I}}{ ext{. for 1 year}} cr
& = { ext{Rs}}.left( {854 - 815}
ight) cr
& = { ext{Rs}}.39 cr
& { ext{S}}{ ext{.I}}{ ext{. for 3 years}} cr
& = { ext{Rs}}{ ext{.}}left( {39 imes 3}
ight) cr
& = { ext{Rs}}{ ext{. }}117 cr
& herefore ext{Principal} cr
& = { ext{Rs}}{ ext{.}}left( {854 - 117}
ight) cr
& = { ext{Rs}}{ ext{. }}698 cr} $$

[#118] In what time will Rs. 3300 becomes Rs. 3399 at 6% per annum interest compounded half-yearly?
Correct Answer

(A) 6 months

Explanation

Solution: $$eqalign{
& P = Rs.,3300 cr
& A = Rs.,3399 cr
& R = 6\% ,{ ext{per}},{ ext{annum}} cr
& { ext{Let}},{ ext{the}},{ ext{time}},{ ext{be}},{ ext{n}},{ ext{years}}{ ext{.}} cr
& { ext{Compound}},{ ext{interest}},{ ext{is}},{ ext{taken}},{ ext{half - yearly}}. cr
& A = P imes {left[ {1 + left( {frac{R}{2} imes 100}
ight)}
ight]^{2n}} cr
& 3399 = 3300{left( {1 + frac{3}{{100}}}
ight)^{2n}} cr
& {left( {1.03}
ight)^{2n}} = frac{{3399}}{{3300}} cr
& {left( {1.03}
ight)^{2n}} = {left( {1.03}
ight)^1} cr
& Thus,,2n = 1,year cr
& n = frac{1}{2}{ ext{year}} = 6,{ ext{months}} cr} $$

[#119] What will be the simple interest on Rs. 700 at 9% per annum for the period from February 5, 1994 to April 18, 1994?
Correct Answer

(A) Rs. 12.60

Explanation

Solution: $$eqalign{
& { ext{Here,}},{ ext{time}},{ ext{interval}},{ ext{is}},{ ext{given}},{ ext{as}}, cr
& { ext{February}},5,,1994,{ ext{to}},{ ext{April}},18,,1994 cr
& = 73,{ ext{days}} = frac{{73}}{{365}} = 0.2,{ ext{years}}. cr
& { ext{Now}},{ ext{interest}} = frac{{PTR}}{{100}} cr
& = frac{{ {700 imes 9 imes 0.2} }}{{100}} cr
& = Rs.,12.60 cr} $$

[#120] A sum was invested at simple interest at a certain interest for 2 years. It would have fetched Rs. 60 more had it been invested at 2% higher rate. What was the sum?
Correct Answer

(A) Rs. 1500

Explanation

Solution: Let the rate be R at which Principal P is invested for 2 years. According to question, {Interest at Rate (R + 2)}% - (interest at rate R%) = Rs. 60 $$frac{{left( {P imes 2 imes left( {R + 2}
ight)}
ight)}}{{100}} - $$ xa0 xa0 $$frac{{left( {P imes 2 imes R}
ight)}}{{100}}$$ xa0 $$ = 60$$ $$eqalign{
& frac{{ {2PR + 4P - 2PR} }}{{100}} = 60 cr
& 4P = 60 imes 100 cr
& { ext{Or}},P = frac{{60 imes 100}}{4} cr
& { ext{Hence}},P = { ext{Rs}}{ ext{.}},1500 cr} $$