Compound Interest - Study Mode

[#151] Kamal took Rs. 6800 as a loan which along with interest is to be repaid in two equal annual installment. If the rate of interest is $$12frac{1}{2}$$ % compounded annually, then the value of each installment is = ?
Correct Answer

(C) Rs. 4050

Explanation

Solution: $$eqalign{
& { ext{Rate of interest}} cr
& { ext{r}} = { ext{12}}frac{1}{2}\% = frac{1}{8} cr} $$ Year Principal Installment ⇒ I 8 ×9 → 9 ×9 ......(i) ⇒ II 64 → 81 ......(ii) Since, installment is equal hence multiply equation (i) by 9 ⇒ Total principal = 72 + 64 = 136 units 136 units → 6800 1 units → 50 81 units → 4050 ⇒ Each installment = Rs. 4050

[#152] A man invests Rs 4000 for 3 years at compound interest. After one year the money amounts to Rs. 4320. What will be the amount (to the nearest rupee) due at the end of 3 years ?
Correct Answer

(B) Rs. 5039

Explanation

Solution: $$eqalign{
& { ext{Le the rate be R }}\% { ext{ p}}{ ext{.a}}{ ext{.}} cr
& { ext{Then,}} cr
& { ext{4000}}left( {1 + frac{{{ ext{R }}}}{{100}}}
ight) = 4320 cr
& Rightarrow 1 + frac{{{ ext{R }}}}{{100}} = frac{{4320}}{{4000}} = frac{{108}}{{100}} cr
& Rightarrow frac{{{ ext{R }}}}{{100}} = frac{8}{{100}} cr
& Rightarrow { ext{R }} = 8 cr
& herefore { ext{Amount after 3 yeras}} cr
& { ext{ = Rs}}{ ext{. }}left[ {4000 + {{left( {1 + frac{8}{{100}}}
ight)}^3}}
ight] cr
& { ext{ = Rs}}{ ext{. }}left( {4000 imes frac{{27}}{{25}} imes frac{{27}}{{25}} imes frac{{27}}{{25}}}
ight) cr
& { ext{ = Rs}}{ ext{. }}left( {frac{{629856}}{{125}}}
ight) cr
& { ext{ = Rs}}{ ext{. }}5038.848 approx 5039 cr} $$

[#153] A sum of Rs. 13360 was borrowed at $${ ext{8}}frac{3}{4}$$ % per annum compound interest and paid back in two years in two equal annual installments. What was the amount of each installment ?
Correct Answer

(B) Rs. 7569

Explanation

Solution: $$eqalign{
& { ext{Rate of interest (r)}} cr
& { ext{ = 8}}frac{3}{4}\% = frac{7}{{80}} = frac{{87 o { ext{ Installment}}}}{{80 o { ext{Principal}}}} cr} $$ ⇒ I 80 ×87 → 87 ×87 ......(i) ⇒ II 6400 → 7569 ......(ii) Since, installment is equal hence multiply equation (i) by 87 ⇒ Total principal = 6960 + 6400 = 13360 ⇒ 13360 units = Rs. 13360 ⇒ 1 units = Rs. 1 ⇒ 7569 units = Rs. 7569 ∴ Each installment = Rs. 7569

[#154] An amount of Rs. 10000 becomes Rs. 14641 in 2 years if the interest is compounded half yearly. What is the rate of compound interest p.c.p.a. ?
Correct Answer

(D) 20%

Explanation

Solution: $$eqalign{
& { ext{Let the rate be R% p}}{ ext{.a}}{ ext{. }} cr
& { ext{Then,}} cr
& { ext{10000}}{left( {1 + frac{{ ext{R}}}{{2 imes 100}}}
ight)^4} = 14641 cr
& Rightarrow {left( {1 + frac{{ ext{R}}}{{200}}}
ight)^4} = frac{{14641}}{{10000}} = {left( {frac{{11}}{{10}}}
ight)^4} cr
& Rightarrow 1 + frac{{ ext{R}}}{{200}} = frac{{11}}{{10}} cr
& Rightarrow frac{{ ext{R}}}{{200}} = frac{1}{{10}} cr
& Rightarrow { ext{R}} = { ext{20% }} cr} $$

[#155] In how many years will a sum of Rs. 800 at 10% per annum compounded semi annually become Rs. 926.10?
Correct Answer

(B) $$1frac{1}{2}$$ years

Explanation

Solution: $$eqalign{
& { ext{Let the time be }}n{ ext{ year}} cr
& { ext{Then,}} cr
& { ext{800}} imes {left( {1 + frac{5}{{100}}}
ight)^{2n}} = 926.10 cr
& Leftrightarrow {left( {1 + frac{5}{{100}}}
ight)^{2n}} = frac{{9261}}{{8000}} cr
& Leftrightarrow {left( {frac{{21}}{{20}}}
ight)^{2n}} = {left( {frac{{21}}{{20}}}
ight)^3} cr
& Leftrightarrow 2n = 3 cr
& Leftrightarrow n = frac{3}{2} cr
& herefore n = 1frac{1}{2}{ ext{years}} cr} $$