Phil Nelson wants to retire in Hawaii when he is 66 years old. Phil is now 48. He believes he will need $350,000 to retire comfortably. To
date, Phil has set aside no retirement money. Assume Phil could
invest at 5% compounded semiannually. How much must Phil invest
today to meet his $350,000 goal?

$60,449

Explanation:

To find the answer, we use the following formula:

FV = PV (1 + i)^n

Where:

FV = Future value (in this case, the $350,000 Phill believes he will need).

PV = Present value (the value we will find).

i = interest rate

n = number of compounding periods (36 periods in this case, because Phill will save for 18 years, and the interest rate compounds semiannually, so 18 x 2 = 36)

Now, we plug the amounts into the formula:

350,000 = PV (1 + 0.05)^36

350,000 = PV (5.79)

350,000 / 5.79 = PV

60,449 = PV

Thus, Phill ll need to invest $60,449 today, to meet his $350,000 goal.