An amount on compound interest is doubled to the original amount in 3 years. In how many yearswill it be eight times its original amount
Question
An amount on compound interest is doubled to the original amount in 3 years.
In how many years will it be eight times its original amount?
Solution
1. Break Down the Problem
We need to find the time it takes for an investment to grow eight times its original amount, given that it doubles in 3 years.
2. Relevant Concepts
The compound interest formula is given by:
Where:
- = amount of money accumulated after n years, including interest.
- = principal amount (the initial amount of money).
- = annual interest rate (decimal).
- = number of years the money is invested or borrowed.
3. Analysis and Detail
-
Since the amount doubles in 3 years:
- Set and :
-
Taking the cube root of both sides:
-
Therefore, the interest rate is:
-
Next, we want to find when the amount will be eight times the principal:
- Set :
-
Substitute :
-
Since :
4. Verify and Summarize
After verifying the calculations, the amount will grow eight times its original amount in 9 years.
Final Answer
The investment will be eight times its original amount in 9 years.
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