Final answer:
Using the formula for continuous compounding, it will take approximately 19.39 years for $8,000 to grow to $15,000 with a 3.25% interest rate.
Step-by-step explanation:
To determine how many years it will take for $8,000 to grow to $15,000 with an interest rate of 3.25% compounded continuously, we can use the formula for continuous compounding:
A = Pe(rt)
where:
- A is the amount of money accumulated after n years, including interest.
- P is the principal amount (the initial amount of money).
- e is the base of the natural logarithm (approximately equal to 2.71828).
- r is the annual interest rate (decimal).
- t is the time in years.
Rearranging the formula to solve for t, we get:
t = (ln(A/P)) / (r)
Now, we plug in the values:
P = $8,000
A = $15,000
r = 3.25% or 0.0325 (in decimal form)
Thus, t = (ln(15,000/8,000)) / (0.0325) ≈ 19.39 years.
Therefore, it will take approximately 19.39 years for $8,000 to grow to $15,000 at a 3.25% interest rate compounded continuously.