Compound Interest - Study Mode

[#76] A sum amount to Rs. 7,562 in 4 years and to Rs. 8,469.44 in 5 years at a certain rate percent per annum, when the interest is compounded yearly. The rate of interest is:
Correct Answer

(B) 12%

Explanation

Solution: $$eqalign{
& 7562,\_\_\_\_\_\_\_\_,8469.44 cr
& { ext{Rate of interest}} = frac{{907.44}}{{7562}} imes 100 = 12\% cr} $$

[#77] A sum of Rs. 12,000 amounts to Rs. 20,736 in 3 years at a certain rate percent per annum interest compounded annually. What will amount of the same sum to in 2 years at the same rate on compound interest?
Correct Answer

(C) Rs. 17,280

Explanation

Solution: Amount in 2 years $$ o 12000 imes frac{6}{5} imes frac{6}{5} = 17280$$

[#78] At what percent is the annual compound interest rate taken such that a certain sum amounts to its 16 times in 4 years?
Correct Answer

(B) 100%

Explanation

Solution: $$ Rightarrow { ext{Rate}} = frac{1}{1} imes 100 = 100{ ext{ Answer}}$$

[#79] A sum of Rs. 10,500 amounts to Rs. 13,650 in 2 years a certain rate percent annum simple interest. The same sum will amount to what in 1 year at the same rate, if the interest in compounded half yearly (nearest to Rs. 1)
Correct Answer

(B) Rs. 12,134

Explanation

Solution: [P = 10500xrightarrow{{,,,,,2{ ext{ year}},,,,,}}13650] $$eqalign{
& 2{ ext{ year}} o 3150 cr
& 3150 = frac{{10500 imes R imes 2}}{{100}} cr
& R = 15\% cr
& A = 10500{left( {1 + frac{{15}}{{200}}}
ight)^2} cr
& = 10500 imes frac{{215 imes 215}}{{200 imes 200}} cr
& = frac{{105 imes 43 imes 43}}{{16}} cr
& = 12134 cr} $$

[#80] A person borrowed some money on compound interest and returned it in 3 equal annual instalments. If the rate of interest is 15% per annum and the annual instalment is Rs. 12,167, then find the sum borrowed.
Correct Answer

(A) Rs. 27,780