Interest - Study Mode

[#51] Find the simple interest on Rs. 5200 for 2 years at 6% per annum.
Correct Answer

(D) Rs. 624

Explanation

Solution: $$eqalign{
& { ext{P = Principal}},{ ext{Amount}} cr
& { ext{T = }},{ ext{Time}},{ ext{period}} cr
& { ext{R = Rate}},{ ext{of}},{ ext{Interest}} cr
& I = frac{{P imes T imes R}}{{100}} cr
& I = frac{{5200 imes 2 imes 6}}{{100}} cr
& I = 624. cr} $$

[#52] Rs. 1200 is lent out at 5% per annum simple interest for 3 years. Find the amount after 3 years.
Correct Answer

(A) Rs. 1380

Explanation

Solution: $$eqalign{
& A = P + I cr
& A = 1200 + {frac{{PTR}}{{100}}} cr
& A = {1200 + {frac{{1200 imes 5 imes 3}}{{100}}} } cr
& { ext{Amount}},,A = Rs.,1380 cr} $$

[#53] Interest obtained on a sum of Rs. 5000 for 3 years is Rs. 1500. Find the rate percent.
Correct Answer

(C) 10%

Explanation

Solution: $$eqalign{
& { ext{Let rate is }}R\% cr
& { ext{We have}}, cr
& I = frac{{PTR}}{{100}} cr
& { ext{Here}},1500 = frac{{5000 imes 3 imes R}}{{100}} cr
& { ext{Thus}},R = 10\% cr} $$

[#54] Rs. 2100 is lent at compound interest of 5% per annum for 2 years. Find the amount after two years.
Correct Answer

(B) Rs. 2315.25

Explanation

Solution: $$eqalign{
& { ext{We}},{ ext{can}},{ ext{use}},{ ext{formula}},{ ext{of}},{ ext{compound}},{ ext{interest}} cr
& A = P imes {left[ {1 + left( {frac{r}{{100}}}
ight)}
ight]^n} cr
& A = 2100 imes {left[ {1 + left( {frac{5}{{100}}}
ight)}
ight]^2} cr
& A = 2100 imes {left[ {frac{{105}}{{100}}}
ight]^2} cr
& A = frac{{ {2100 imes 11025} }}{{10000}} cr
& { ext{Hence,}},{ ext{Amount}},A = Rs.,2315.25 cr} $$

[#55] Find the difference between the simple interest and the compound interest at 5% per annum for 2 years on principal of Rs. 2000.
Correct Answer

(A) 5

Explanation

Solution: $$eqalign{
& { ext{The}},{ ext{difference}},{ ext{between}},{ ext{compound}},{ ext{interest}},{ ext{and}} cr
& { ext{simple}},{ ext{interest}},{ ext{over}},{ ext{two}},{ ext{years}},{ ext{is}},{ ext{given}},{ ext{by}} cr
& frac{{{{Pr }^2}}}{{{{100}^2}}},or,P{left( {frac{r}{{100}}}
ight)^2} cr
& { ext{Here,}},{ ext{Principal}},left( P
ight) = Rs.,2000 cr
& { ext{Rate}},left( r
ight) = 5\% cr
& { ext{Now}},{ ext{difference}}, cr
& D = frac{{ {2000 imes 5 imes 5} }}{{ {100 imes 100} }} cr
& D = Rs.,5 cr} $$