You have a goal of having $100,000 five years from today.The return on the investment is expected to be 8% and will be compounded semiannually.The amount that needs to be invested today is closest to:
A)$67,556.
B)$56,420.
C)$71,195.
D)$35,034.

Question

Quizplus · Accepted Answer

To find the present value (the amount that needs to be invested today) to achieve a future value of $100,000 in 5 years with an 8% annual interest rate compounded semiannually, we use the formula for the present value of a single sum: $PV = \frac{FV}{(1 + r/n)^{nt}}$, where PV is the present value, FV is the future value, r is the annual interest rate, n is the number of compounding periods per year, and t is the time in years. Plugging in the values: $PV = \frac{100,000}{(1 + 0.08/2)^{2*5}} = \frac{100,000}{(1 + 0.04)^{10}} ≈ $67,556$.

You Have a Goal of Having $100,000 Five Years from Today.The