Final answer:
To find the balance after 16 years, we use the continuous compounding formula A = P * e^(rt). With a principal of $8750, a rate of 9%, and a time of 16 years, the balance is approximately $36930.88.
Step-by-step explanation:
To calculate the balance of $8750 invested at a rate of 9% compounded continuously for 16 years, we use the formula for continuous compounding, which is A = P * e^(rt), where:
- P is the principal amount ($8750)
- r is the annual interest rate (9% or 0.09)
- t is the time in years (16)
- e is the base of the natural logarithms (approximately 2.71828)
Using the formula:
A = 8750 * e^(0.09 * 16)
Calculating this, we get:
A ≈ $8750 * e^(1.44)
A ≈ $8750 * 4.2207
A ≈ $36930.88
After 16 years, the balance would be approximately $36930.88.