A company invests $15,000.00 in an account that compounds interest annually. After two years, the account is worth $16,099.44. Use the function, where r is the annual interest rate, P is the principal, and A is the amount of money after t years. What is the interest rate of the account? (1 point) Responses
1.04%
3.6%
5.4%
7.3%
To solve for the interest rate, we need to use the formula for compound interest:
A = P(1 + r)^t
Where:
A = Final amount after t years ($16,099.44)
P = Principal amount ($15,000.00)
r = Annual interest rate
t = Number of years (2 years)
Substitute the values into the formula:
16,099.44 = 15,000(1 + r)^2
Divide both sides by 15,000:
16,099.44 / 15,000 = (1 + r)^2
1.0733 = (1 + r)^2
Take the square root of both sides to solve for r:
√1.0733 = 1 + r
1.036 = 1 + r
r = 0.036 or 3.6%
Therefore, the interest rate of the account is 3.6%.