Final answer:
To find out how much Madeline would need to invest, we can use the formula for compound interest. Madeline would need to invest approximately $10,492 to the nearest ten dollars.
Step-by-step explanation:
To find out how much Madeline would need to invest, we can use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the amount in the account after t years, P is the principal amount (initial investment), r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the number of years.
In this case, Madeline wants the value of the account to reach $16,600 in 12 years with an interest rate of 4.4% compounded annually. So we can substitute A = 16600, r = 0.044, n = 1, and t = 12 into the formula:
16600 = P(1 + 0.044/1)^(1*12)
Simplifying this equation, we have:
16600 = P(1.044)^12
Next, we can isolate P by dividing both sides of the equation by (1.044)^12:
P = 16600 / (1.044)^12
Using a calculator to evaluate this expression, we find that P is approximately $10,492.11. Therefore, Madeline would need to invest $10,492 to the nearest ten dollars.