Compound Interest Sum Growth Calculation
This problem concerns the exponential growth of a sum under compound interest.
Understanding Growth Factors
Let the initial principal sum be denoted by P.
- The problem states that the sum becomes 4 times its initial value (4P) in a period of 3 years.
- This implies a growth factor of 4 over every 3-year period, assuming a constant interest rate.
- The goal is to determine the time required for the sum to become 64 times its initial value (64P).
Calculating Time for 64 Times Growth
We need to relate the target growth factor (64) to the known growth factor (4).
- We can express 64 as a power of 4: $ 64 = 4 \times 4 \times 4 = 4^3 $
- This means the process that multiplies the sum by 4 needs to be repeated 3 times to achieve a total multiplication factor of 64.
- Since each 3-year period results in the sum multiplying by 4, three such periods are required.
- The total time is calculated as: $ \text{Total Time} = (\text{Number of 4x growth cycles}) \times (\text{Time per cycle}) $ $ \text{Total Time} = 3 \times 3 \text{ years} $ $ \text{Total Time} = 9 \text{ years} $
Thus, the sum will become 64 times its original value in 9 years.
Similar Questions
- There is 60% increase in an amount in 6 years at simple interest. What will be the compound interest of ₹10,000 after 3 years at the same rate?
- The difference between the compound interest and the simple interest accrued, at the same rate of interest, on an amount of ₹16,000 in 2 years was ₹1,000. What was the rate of interest percent per annum?
- A deposited ₹8,000 in a bank at 8% per annum simple interest. B deposited ₹6,000 at 10% compound interest per annum. After 3 years the difference between their interest will be:
Find the interest (in ₹) on ₹8,000 at 10% per annum compounded half yearly for $1\frac{1}{2}$ years.
- Find the compound interest on ₹1,200 at 12% p.a. for 6 months compounded quarterly.
- A sum of money was lent on compound interest. It became ₹500 at the end of the first year and ₹550 at the end of second year. Find the rate of compound interest per annum.
- Simple interest on a sum of money, at $5\%$ per annum for 2 years, is ₹50. The compound interest on the same sum for the same period at the same interest rate is:
- If the difference between the compound interest and the simple interest on a certain sum of money at 8 % p.a. for 2 years is ₹240, then the sum of money is:
- The compound interest on a sum of ₹7,500 for 2 years at 4 % p.a. is
The difference between the compound interest and the simple interest on a principal sum of $₹24,000$ in $2$ years at same rate of interest is $₹60$. The rate of interest is:
Important Questions from Simple and Compound Intrest
Amit had invested same amount of sums at simple as well as compound interest, compounded annually. The time period of investment for both the sums was 2 years and rate of interest too was the same, 4% per annum. At the end, he found a difference of ₹43 in both the interests received. What were the sums (in ₹) invested?
When the difference between compound interest, compounded annually, and simple interest for three years is ₹186 at 10% interest per annum, the principal is ₹______.
- When the difference between compound interest, compounded annually, and simple interest for three years is ₹217 at 10% interest per annum, the principal is ₹______.
- When the difference between compound interest, compounded annually, and simple interest for three years is ₹228 at 4% interest per annum, the principal is ₹______.
- The difference between the compound interest, compounded annually and the simple interest if ₹17,700 is deposited at 4% rate of interest per annum for 2 years is:
