Final answer:
To determine the number of years required for an initial deposit to triple with an 11% annual interest rate, one can use the compound interest formula and solve for time using logarithms.
Step-by-step explanation:
The question involves determining the number of years needed for an initial deposit to triple in value with an annual interest rate of 11%. To solve this problem, we can apply the formula for compound interest, which is A = P(1 + r/n)^(nt), where:
- A is the amount of money accumulated after n years, including interest.
- P is the principal amount (the initial amount of money).
- r is the annual interest rate (decimal).
- n is the number of times that interest is compounded per year.
- t is the time in years.
Since the money needs to treble, we can set A to 3P. The interest is not compounded more frequently than annually in this case, so n will be 1. Therefore, the equation simplifies to:
3P = P(1 + r)^t
We can cancel P from both sides and solve for t:
3 = (1 + 0.11)^t
To find t, we take the natural logarithm of both sides:
ln(3) = ln((1 + 0.11)^t)
ln(3) = t * ln(1.11)
t = ln(3) / ln(1.11)
By calculating the logarithms, we can find the number of years t required for the money to treble.