A sum of money becomes three times its original value in 8 years when invested at compound interest. In how many years will the same sum become 81 times its original value at the same rate of interest?
32 years
Let the rate factor be \((1+r)\). Becoming three times in 8 years means \((1+r)^8 = 3\).
We need the time t for the sum to become 81 times, i.e., \((1+r)^t = 81\).
Since \(81 = 3^4\), we can write \((1+r)^t = \left[(1+r)^8\right]^4 = (1+r)^{32}\).
Comparing powers, \(t = 32\) years.
Important Questions from Compound Interest
A person borrowed Rs. 10000 on compound interest at the rate of 40 percent per annum. If the interest is compounded half yearly, then what will be the amount to be paid after 1.5 years?
In how many years will a sum of Rs.1875 amount to Rs.2187 at 8 percent p.a. compound interest?
A sum of money has increased by 45% in 9 years at simple interest. What will be the compound interest of Rs. 12,000 after 3 years at the same rate?
At a certain rate of compound interest a certain sum amounts to Rs. 64800 in 4 years and Rs. 93312 in 6 years. What is the compound interest earned in fifth year?
Karuna has an option to invest in the following three schemes. If she wants to invest Rs P, then which scheme will be most beneficial for her?
Scheme that comes with lower interest rates and terms;
I. 28% p.a. interest, compounded every quarter, for one year.
II. 28% p.a. interest, compounded every half year, for one year.
III. 28% p.a. interest, for one year, compounded every year.
