Suppose an investment account is opened with an initial deposit of $12,000 earning 7.2% interest compounded continuously. How much will the account be worth after 30 years?
Answer
Investment Growth with Continuous Compounding
When interest is compounded continuously, the investment grows exponentially over time. The formula to calculate the future value is:
A = P × ert
- A = Final amount
- P = Initial principal ($12,000)
- r = Annual interest rate (7.2% = 0.072)
- t = Time in years (30)
- e = Euler’s number ≈ 2.71828
🔢 Step-by-Step Calculation
Substitute the given values into the formula:
A = 12,000 × e0.072 × 30 = 12,000 × e2.16
Calculate the exponent:
e2.16 ≈ 8.6657
Now compute the final value:
A ≈ 12,000 × 8.6657 ≈ $103,988.40
✅ Final Answer:
The investment will be worth approximately $103,988.40 after 30 years with continuous compounding at 7.2% annual interest.
Note: Continuous compounding results in a slightly higher return than yearly or monthly compounding due to the use of Euler’s number (e) in exponential growth.