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
At what rate percent per annum will Rs. 7200 amount to Rs. 7938 in one year, if interest is compounded half yearly?
What is the compound interest (in Rs.) on a sum of Rs. 8192 for \(1 \frac{1}{4}\) years at 15% per annum, if interest is compounded 5-monthly ?
What is the difference (in Rs.) between the interests on Rs. 50,000 for one year at 8% per annum compounded half yearly and yearly?
A sum of money becomes Rs. 11,880 after 4 years and Rs. 17,820 after 6 years on compound interest, if the interest is compounded annually. What is the half of the sum (in Rs.)?
A sum invested at compound interest amounts to Rs. 7,800 in 3 years and Rs. 11,232 in 5 years. What is the rate per cent?
