The interest earned on $5,600 deposited for 5 years at an annual interest rate compounded continuously is approximately $1177.60.
To find the interest earned on $5,600 deposited for 5 years at an annual interest rate compounded continuously, we can use the formula:
A = P * e^(rt)
where:
A is the final amount after 5 years
P is the principal amount ($5,600)
e is Euler's number (approximately 2.7183)
r is the annual interest rate (as a decimal, not a percentage)
t is the time in years (5 years)
1: Convert the interest rate to a decimal
The interest rate is given as an annual rate, but we need it as a decimal for the formula. So, divide the annual rate by 100:
r = 0.05
2: Calculate the final amount (A)
A = 5600 * e^(0.05 * 5)
A ≈ 6777.60
3: Calculate the interest earned
The interest earned is the difference between the final amount (A) and the principal amount (P):
Interest earned = A - P
Interest earned ≈ 6777.60 - 5600
Interest earned ≈ $1177.60
Therefore, the interest earned on $5,600 deposited for 5 years at an annual interest rate compounded continuously is approximately $1177.60.