I can't figure this out, please help...
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 = 1.073296
1+r = 1.036
r = 0.036
So, the rate is 3.6%
3.6%
To find the interest rate of the account, we can rearrange the formula A = P(1 + r)t to solve for r.
Given:
P = $15,000 (principal)
A = $16,099.44 (amount after two years)
t = 2 years
We can substitute these values into the formula and solve for r:
$16,099.44 = $15,000(1 + r)^2
First, divide both sides of the equation by $15,000:
$16,099.44 / $15,000 = (1 + r)^2
Next, take the square root of both sides of the equation:
√($16,099.44 / $15,000) = 1 + r
Now, subtract 1 from both sides of the equation:
√($16,099.44 / $15,000) - 1 = r
Using a calculator, you can evaluate the left-hand side of the equation to find the value of r.
r is approximately 0.036 or 3.6%.
Therefore, the interest rate of the account is 3.6%.
The correct answer is: 3.6%