Compound Interest - Study Mode

[#96] The compound interest on Rs. 4,000 after 3 year is Rs. 630.50. Then the rate of interest compounded yearly is:
Correct Answer

(B) 5%

Explanation

Solution: $$eqalign{
& 4630.50 = 4000{left( {1 + frac{R}{{100}}}
ight)^3} cr
& 9261 = 8000{left( {1 + frac{R}{{100}}}
ight)^3} cr
& frac{{9261}}{{8000}} = {left( {1 + frac{R}{{100}}}
ight)^3} cr
& {left( {frac{{21}}{{20}}}
ight)^3} = {left( {1 + frac{R}{{100}}}
ight)^3} cr
& frac{{21}}{{20}} = left( {1 + frac{R}{{100}}}
ight) cr
& frac{1}{{20}} = frac{R}{{100}} cr
& R = 5 cr} $$

[#97] Vipul and Manish invested the sum on Rs. 15000 and Rs. 20000 at the rate of 20 percent p.a and 30 percent p.a. respectively on compound interest (compounding annually). If time period is 3 years for both, then what will be the total compound interest earned by Vipul and Manish?
Correct Answer

(D) Rs. 34860

Explanation

Solution: $$eqalign{
& 15000left[ {{{left( {1 + frac{{20}}{{100}}}
ight)}^3} - 1}
ight] + 20000left[ {{{left( {1 + frac{{30}}{{100}}}
ight)}^3} - 1}
ight] cr
& = 15000left( {frac{{216}}{{125}} - 1}
ight) + 20000left( {frac{{2197}}{{1000}} - 1}
ight) cr
& = 15000 imes frac{{91}}{{125}} + 20000 imes frac{{1197}}{{1000}} cr
& = 10920 + 23940 cr
& = { ext{Rs}}{ ext{. }}34860 cr} $$

[#98] The simple interest on a sum of money at 10% per annum for 2 years is Rs. 8,100. What would be the compound interest (in Rs.) on the same sum for the same period at 15% p.a, when the interest is compound yearly?
Correct Answer

(A) 13061.25

Explanation

Solution: R = 10%, T = 2 year, SI = Rs. 8100 $$8100 = frac{{{ ext{P}} imes 10 imes 2}}{{100}}$$ 40500 = P Now same principal R% = 15% T = 2 year CI = ? $$15\% = frac{3}{{20}}$$ $${ ext{CI}} = frac{{129 imes 405}}{4} = 13061.25$$

[#99] A sum amounts to Rs. 18,600 after 3 years and to Rs. 27,900 after 6 years, at a certain rate percent p.a, when the interest is compounded annually. The sum is:
Correct Answer

(B) Rs. 12,400

Explanation

Solution: $$eqalign{
& { ext{P}} imes frac{{27,900}}{{18,600}} = 18,600 cr
& { ext{P}} = frac{{18,600 imes 186}}{{279}} cr
& { ext{P}} = 12,400 cr} $$

[#100] A certain sum amounts to Rs. 4,205.55 at 15% p.a. in $$2frac{2}{5}$$xa0years, interest compounded yearly. The sum is:
Correct Answer

(B) Rs. 3,000