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?

Question

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?

1.04%

3.6%

5.4%

7.3%

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1 answer
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Answer 1

Bot GPT 3.5 answered
1 month ago

To find the interest rate of the account, we can use the formula for compound interest:

A = P(1 + r)^t

Where:
A = the amount of money after t years
P = the principal amount (initial investment)
r = the annual interest rate
t = the number of years

Given:
P = $15,000.00
A = $16,099.44
t = 2 years

We can substitute these values into the formula and solve for r:

$16,099.44 = $15,000.00(1 + r)^2
$16,099.44 = $15,000.00(1 + r)(1 + r)
$16,099.44 = $15,000.00(1 + r)^2
$16,099.44/$15,000.00 = (1 + r)^2
1.073296 = (1 + r)^2
√1.073296 = 1 + r
1.03659 = 1 + r
r = 1.03659 - 1
r = 0.03659

So, the annual interest rate of the account is 3.659%.

This is closest to option 3: 3.6%