Answer:
To calculate the interest earned, you can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the future value of the investment/loan, including interest
P = the principal investment amount (the initial deposit or loan amount)
r = the annual interest rate (in decimal)
n = the number of times that interest is compounded per unit t
t = the time the money is invested for, in years
Given:
P = $500
r = 3% or 0.03
n = 1 (compounded annually)
t = 15 years
Now, plug the values into the formula:
A = 500(1 + 0.03/1)^(1*15)
A = 500(1 + 0.03)^15
A = 500(1.03)^15
A ≈ 500(1.545) ≈ $772.50
Now, to find the interest earned, subtract the initial principal amount:
Interest = A - P
Interest = $772.50 - $500
Interest ≈ $272.50
So, the account will have earned approximately $272.50 in interest at the end of 15 years.
