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
r = 0.36
Isn't that 0.036 or 3.6%
Dr Bob, you are correct. I solved it correctly earlier, and got impatient when it popped up again.
My bad.
Thanks so very much
To find the interest rate of the account, we need to rearrange the formula A = P(1 + r)t to solve for r.
Given:
P (principal) = $15,000.00
A (amount after 2 years) = $16,099.44
t (time) = 2 years
We substitute these values into the equation:
$16,099.44 = $15,000.00(1 + r)^2
To solve for r, we need to rearrange the equation. First, divide both sides of the equation by P:
$16,099.44 / $15,000.00 = (1 + r)^2
Next, take the square root of both sides of the equation:
√($16,099.44 / $15,000.00) = 1 + r
Now, subtract 1 from both sides of the equation:
√($16,099.44 / $15,000.00) - 1 = r
Calculating the left-hand side of the equation gives us:
√(1.073296) - 1 = r
Simplifying further:
1.035690 - 1 = r
0.035690 = r
Therefore, the interest rate of the account is 3.5690% (rounded to two decimal places).
Out of the answer choices provided, the closest match is 3.6%.