Final answer:
Adrianna should invest around $8724.61 now at a 4.6% interest rate compounded semiannually to meet her goal of saving $10,000 in 3 years.
Step-by-step explanation:
To calculate the amount of money Adrianna should invest now, we can use the formula for compound interest:
A = P(1 + r/n)^(nt), { where A is the future value, P is the principal amount (the amount to be invested), r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.
In this case, Adrianna wants to have $10,000 in 3 years, so A = $10,000, r = 4.6% (or 0.046), and n = 2 (as interest is compounded semiannually).
We need to solve for P.
Plugging in the values into the formula, we get:
$10,000 = P(1 + 0.046/2)^(2*3)
Simplifying the equation gives:
$10,000 = P(1.023)^6
Solving for P, we divide both sides of the equation by (1.023)^6:
P = $10,000 / (1.023)^6
We find that P is approximately $8724.61
Therefore, Adrianna should invest around $8724.61 to meet her goal of having $10,000 in 3 years.