Interest - Study Mode
[#36] In how many years will the simple interest on a sum of money be equal to the principle at rate of $$12frac{2}{4}\% $$ xa0per annum?
Correct Answer
(C) 8 years
Explanation
Solution: $$eqalign{
& 1 = 1 imes frac{{50}}{{400}} imes t cr
& t = 8{ ext{ years}} cr} $$
[#37] What is the present value of Rs. 10,000 received in 2 years, if the interest rate is 12% per year discounted semi-annually?
Correct Answer
(C) Rs. 7,920.94
Explanation
Solution: $$eqalign{
& { ext{Amount received in 2 years}} = { ext{Rs}}{ ext{. }}10,000 cr
& { ext{Interest rate}} = 12\% { ext{ per year}} cr
& { ext{Time}} = 2{ ext{ years}} cr
& {x08f{Formula ,used:}} cr
& { ext{Amount}} = { ext{Principal}}{left[ {1 + left( {frac{R}{{100}}}
ight)}
ight]^n} cr
& {x08f{Calculation:}} cr
& A = 10000 cr
& R = 6\% { ext{ }}left( {{ ext{semi - annually}}}
ight) cr
& n = 4\% { ext{ }}left( {{ ext{semi - annually}}}
ight) cr
& { ext{Thus,}} cr
& Rightarrow 10000 = P{left[ {1 + left( {frac{6}{{100}}}
ight)}
ight]^4} cr
& Rightarrow 10000 = P{left[ {frac{{106}}{{100}}}
ight]^4} cr
& Rightarrow 10000 = P imes {left( {1.06}
ight)^4} cr
& Rightarrow P = frac{{10000}}{{{{1.06}^4}}} cr
& Rightarrow P = 7920.9426 cr
& Rightarrow P = { ext{Rs}}{ ext{. }}7920.94 cr
& { ext{Hence, the correct answer is Rs}}{ ext{. 7,920}}{ ext{.94}} cr} $$
[#38] An amount of Rs. 12,000 was borrowed at some rate of simple interest. After four months, Rs. 6,000 more were added to it and the rate of interest on the total principal was doubled from the previous rate. At the end of the year, Rs. 2,800 was paid as interest, calculate the rate of interest initially charged?
Correct Answer
(D) 10%
Explanation
Solution: $$eqalign{
& { ext{Let, Rate}} = 12x\% { ext{ per year}} cr
& frac{{12000 imes 4x}}{{100}} + frac{{18000 imes 16x}}{{100}} = 2800 cr
& 480x + 2880x = 2800 cr
& 3360x = 2800 cr
& x = frac{{10}}{{12}} cr
& { ext{Rate}} = 12x cr
& = frac{{10}}{{12}} imes 12 cr
& = 10\% cr} $$
[#39] Damani purchased an item costing Rs. 7,500 and paid Rs. 3,500 as a down payment for the same. If the simple interest charged for the remaining amount is 9% per annum and Damani cleared all dues after 4 months of the purchase, how much did Damani pay after 4 months as interest?
Correct Answer
(A) Rs. 120
Explanation
Solution: $$eqalign{
& { ext{She paid}} = 3500 cr
& { ext{Left amount}} = 7500 - 3500 = 4000 cr
& { ext{S}}{ ext{.I}}{ ext{.}} = frac{{4000 imes 9 imes 4}}{{100 imes 12}} = 120 cr} $$
[#40] A sum of money invested at simple interest becomes 17/10 of itself in 2 years and 6 months. What is the rate of interest per annum?
Correct Answer
(C) 28%
Explanation
Solution: $$eqalign{
& { ext{S}}{ ext{.I}}{ ext{.}} = frac{{P imes r imes t}}{{100}} cr
& 7 = frac{{10 imes r imes 5}}{{2 imes 100}} cr
& r = 28\% cr} $$