Understanding the Problem
To determine how many years it will take for a sum of money to triple at the same rate of simple interest, we start by analyzing the information given.
Key Information
- The amount doubles in 6 years.
- We need to find the time required for it to become three times its original amount.
Calculating the Rate of Simple Interest
1. Doubling in 6 Years:
- If the principal amount (P) doubles in 6 years, the total amount at the end of 6 years is 2P.
- Using the formula for simple interest:
\[ A = P + SI \]
where \( SI = \frac{P \times r \times t}{100} \)
Therefore,
\[ 2P = P + \frac{P \times r \times 6}{100} \]
Simplifying gives:
\[ P = \frac{P \times r \times 6}{100} \]
or
\[ r = \frac{100}{6} = 16.67\% \text{ per annum} \]
Finding Time to Triple the Amount
2. Tripling the Amount:
- We need to find the time (t) when \( A = 3P \):
\[ 3P = P + \frac{P \times r \times t}{100} \]
\[ 3P - P = \frac{P \times r \times t}{100} \]
\[ 2P = \frac{P \times r \times t}{100} \]
Canceling \( P \) (assuming \( P \neq 0 \)) gives:
\[ 2 = \frac{r \times t}{100} \]
Substituting \( r = 16.67 \):
\[ 2 = \frac{16.67 \times t}{100} \]
\[ t = \frac{2 \times 100}{16.67} \approx 12 \text{ years} \]
Conclusion
It will take approximately 12 years for the sum of money to triple at the same rate of simple interest.