Final answer:
Mackenzie would need to invest approximately $97,560, to the nearest ten dollars, in an account with a 6.5% interest rate compounded monthly to have $194,000 in 11 years.
Step-by-step explanation:
To determine how much Mackenzie would need to invest to have $194,000 in her account in 11 years at an interest rate of 6.5% compounded monthly, we need to use the formula for compound interest:
P = A / (1 + r/n)(nt)
Where:
P is the principal amount (the initial amount of money)
A is the amount of money accumulated after n years, including interest.
r is the annual interest rate (decimal)
n is the number of times that interest is compounded per year
t is the time the money is invested for, in years
Let's plug in the given values:
A = $194,000
r = 0.065 (6.5% as a decimal)
n = 12 (since interest is compounded monthly)
t = 11 (the number of years the money will be invested)
We can now solve for P:
P = 194,000 / (1 + 0.065/12)(12*11)
Calculating the above expression with a calculator, we get:
P ≈ $97,560.29
To the nearest ten dollars, Mackenzie would need to invest $97,560.