Compound Interest - Study Mode
[#56] What does Rs. 250 amounts to in 2 years with compound interest at the rate of 4% in the 1 st year and 8% in the second year ?
Correct Answer
(B) Rs. 280.80
Explanation
Solution: $$eqalign{
& { ext{Principal = Rs 250}} cr
& {{ ext{R}}_1} = 4\% ,,,,,,,,,,{{ ext{R}}_2} = 8\% cr
& { ext{Amount}},{ ext{after}}{1^{st}},{ ext{year}} cr
& = 250left( {1 + frac{4}{{100}}}
ight) = { ext{Rs}}{ ext{. }}260 cr
& { ext{Amount after }}{{ ext{2}}^{{ ext{nd}}}}{ ext{ year}} cr
& { ext{ = }}260left( {1 + frac{8}{{100}}}
ight) cr
& = { ext{Rs}}{ ext{. }}280.80 cr} $$
[#57] The compound interest on a certain sum of money for 2 years at 5% is Rs. 328, then the sum is = ?
Correct Answer
(C) Rs. 3200
Explanation
Solution: For a first result cross check with option (Go with option (C) and check it.) Principal is Rs. 3200 3200 of 5% for 1 st year = 160 then, principal = 3200 + 160 = 3360 3360 of 5% for 2 nd year = 168 ∴ Interest = 160 + 168 = 328
[#58] The compound interest on a certain sum of money for 2 years at 5% per annum is Rs 410. The simple interest on the same sum at the same rate and for the same time is = ?
Correct Answer
(A) Rs. 400
Explanation
Solution: $$eqalign{
& { ext{Rate of interest 5}}\% cr
& = frac{1}{{20}} cr
& { ext{Let principal}} cr
& { ext{ = }}{left( {20}
ight)^2}{ ext{ = 400 units}} cr
& Rightarrow { ext{ Total compound interest }} cr
& { ext{41 Units }} o { ext{Rs. 410 }} cr
& { ext{1 Units }} o { ext{Rs. 10 }} cr
& { ext{400 Units }} o { ext{Rs. 400 }} cr
& { ext{Total simple interest}} cr
& { ext{ = Rs. 400}} cr} $$ Alternate Total compound interest for 2 years at 5% p.a. $$eqalign{
& { ext{ = 5 + 5 + }}frac{{5 imes 5}}{{100}} = 10.25\% cr
& { ext{Total simple interest}} cr
& = 10\% cr
& Rightarrow 10.25\% o 410 cr
& Rightarrow 10\% o 400 cr
& { ext{Simple interest}} cr
& { ext{ = Rs}}{ ext{. 400}} cr} $$
[#59] A sum of money lent out at compound interest increases in value by 50% in 5 years. A person wants to lend three different sums x, y and z for 10, 15 and 20 years respectively at the above rate in such a way that he gets back equal sums at the end of their respective periods. The ratio x : y : z is = ?
Correct Answer
(C) 9 : 6 : 4
Explanation
Solution: $$eqalign{
& P{left( {1 + frac{R}{{100}}}
ight)^5} = 150\% ,{ ext{of }}P = frac{3}{2}P cr
& Rightarrow {left( {1 + frac{R}{{100}}}
ight)^5} = frac{3}{2} cr} $$ $$x{left( {1 + frac{R}{{100}}}
ight)^{10}} = y{left( {1 + frac{R}{{100}}}
ight)^{15}} = $$ xa0 xa0 xa0 $$z{left( {1 + frac{R}{{100}}}
ight)^{20}}$$ $$ Rightarrow x{left{ {{{left( {1 + frac{R}{{100}}}
ight)}^5}}
ight}^2} = $$ xa0 xa0xa0 $$y{left{ {{{left( {1 + frac{R}{{100}}}
ight)}^5}}
ight}^3} = $$ xa0 xa0 $$z{left{ {{{left( {1 + frac{R}{{100}}}
ight)}^5}}
ight}^4}$$ $$eqalign{
& Rightarrow x imes {left( {frac{3}{2}}
ight)^2} = y imes {left( {frac{3}{2}}
ight)^3} = z imes {left( {frac{3}{2}}
ight)^4} cr
& Rightarrow frac{{9x}}{4} = frac{{27y}}{8} = frac{{81z}}{{16}} = k({ ext{say}}) cr
& Rightarrow x = frac{{4k}}{9},y = frac{{8k}}{{27}},z = frac{{16k}}{{81}} cr
& Rightarrow x:y:z = frac{{4k}}{9}:frac{{8k}}{{27}}:frac{{16k}}{{81}} cr
& Rightarrow x:y:z = 36:24:16 cr
& Rightarrow x:y:z = 9:6:4 cr} $$
[#60] Under the Rural Housing Scheme, the Delhi Development Authority (DDA) allotted a house to Kamal Raj for Rs. 126100. This payment is to be made in three equal annual instalments. If the money is reckoned at 5% per annum compound interest, then how much is to be paid by Kamal Raj in each instalment ?
Correct Answer
(B) Rs. 46305
Explanation
Solution: Let the value of each instalment be Rs. x Then, (P.W. of Rs. x due 1 year hence) + (P.W. of Rs. x due 2 year hence) + (P.W. of Rs. x due 3 year hence) = 126100 $$eqalign{
& Rightarrow frac{x}{{left( {1 + frac{5}{{100}}}
ight)}} + frac{x}{{{{left( {1 + frac{5}{{100}}}
ight)}^2}}} + frac{x}{{{{left( {1 + frac{5}{{100}}}
ight)}^3}}} = 126100 cr
& Rightarrow frac{{20x}}{{21}} + frac{{400x}}{{441}} + frac{{8000x}}{{9261}} = 126100 cr
& Rightarrow frac{{8820x + 8400x + 8000x}}{{9261}} = 126100 cr
& Rightarrow frac{{25220x}}{{9261}} = 126100 cr
& Rightarrow x = left( {frac{{126100 imes 9261}}{{25220}}}
ight) cr
& Rightarrow x = 46305 cr} $$