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 in which 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? A = P(1 + r)t
• 1.04%
• 3.6%
• 5.4%
• 7.3%
15000(1+r)^2 = 16099.44
(1+r)^2 = 1.0733
1+r = 1.036
r = 0.036
To find the interest rate of the account, we can rearrange the formula:
A = P(1 + r)^t
Given:
P = $15,000.00
A = $16,099.44
t = 2 years
Substituting these values into the formula, we have:
$16,099.44 = $15,000.00(1 + r)^2
Now, let's solve for r:
Divide both sides of the equation by $15,000.00:
$16,099.44/$15,000.00 = (1 + r)^2
1.073296 = (1 + r)^2
Take the square root of both sides:
√1.073296 = √(1 + r)^2
1.036 = 1 + r
Subtract 1 from both sides:
1.036 - 1 = r
r = 0.036, or 3.6%
Therefore, the interest rate of the account is 3.6%.