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 principle, and A is the amount of money after t years. What is the interest rate of the account? A=P(1+r)^t (1 point)
A= P(1+r)^t
16099.44= 15000(1+r)^2
16099.44/15000 = (1+r)^2
sqrt((16099.44/15000) = 1+ r
sqrt(166099.44/1500) -1 = r
r = 3.6%
To find the interest rate (r), we can rearrange the formula and solve for r.
The formula given is: A = P(1 + r)^t
Given values:
P = $15,000.00
A = $16,099.44
t = 2 years
Substituting the given values into the formula, we get:
$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
Simplify:
1.073296 = (1 + r)^2
Take the square root of both sides:
√(1.073296) = 1 + r
1.035719 = 1 + r
Subtract 1 from both sides:
1.035719 - 1 = r
r ≈ 0.035719
The interest rate of the account is approximately 0.0357 or 3.57% (rounded to two decimal places).