Final answer:
The amount owed on a $3400 loan with a 4.5% annual interest rate, compounded continuously for three years, is approximately $3891.85.
Step-by-step explanation:
To calculate the amount owed on a loan of $3400 with an interest rate of 4.5% per year, compounded continuously, and assuming no payments are made until the end of three years, we use the formula for continuous compounding, A = Pert, where:
P is the principal amount ($3400)
r is the annual interest rate (0.045)
t is the time in years (3)
e is the base of the natural logarithm (approximately 2.71828)
Plugging these values into the formula:
A = 3400e0.045 * 3
To find the amount A, we calculate this expression using a scientific calculator or a computer:
A ≈ 3400 * e0.135
A ≈ 3400 * 2.718280.135
A ≈ 3400 * 1.14472
A ≈ $3891.85
Therefore, the amount owed after three years is approximately $3891.85, when rounded to the nearest cent.