Yes, you read the question correctly. We are given a future value of $2000 and we need to find the present value. To do this, we can rearrange the compound interest formula to solve for the present value (P).
The formula for compound interest is: FV = PV * (1 + r/n)^(n*t), where:
FV = Future value
PV = Present value
r = Interest rate
n = Number of times compounded per year
t = Number of years
In this case, the future value (FV) is $2000, the interest rate (r) is 9%, the number of times compounded per year (n) is 2 (semiannually), and the number of years (t) is 8.
So, the formula becomes: $2000 = P * (1 + 0.09/2)^(2*8)
To solve for P, divide both sides of the equation by (1 + 0.09/2)^(2*8):
P = $2000 / (1 + 0.09/2)^(2*8)
Simplifying the equation:
P = $2000 / (1.045)^16
Now, calculate (1.045)^16 using a calculator:
P ≈ $2000 / 1.8389
P ≈ $1089.71
So, approximately $1089.71 should be invested now in order to accumulate $2000 at a 9% compound interest rate semiannually for 8 years.