An investment of $750 will be worth $1500 after 12 years of continuous compounding at a fixed interest rate. What is that interest rate?
Question
An investment of 1500 after 12 years of continuous compounding at a fixed interest rate. What is that interest rate?
Solution
To solve this problem, we can use the formula for continuous compounding, which is:
A = P * e^(rt)
where: A = the amount of money accumulated after n years, including interest. P = the principal amount (the initial amount of money) r = annual interest rate (in decimal) t = time (the number of years)
In this case, we know that A = 750, and t = 12 years. We want to find r.
First, we can rearrange the formula to solve for r:
r = ln(A/P) / t
Substituting the given values:
r = ln(1500/750) / 12
r = ln(2) / 12
r ≈ 0.0577
So, the annual interest rate is approximately 5.77%.
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