Question

Checkm Earl Ezekiel wants to retire in San Diego when he is 65 years old. Earl is now 46. He believes he will need $320,000 to retire comfortably. To date, Earl has set aside no retirement money. Assume Earl gets 4% interest compounded semiannually. How much must Earl invest today to meet his $320,000 goal?

Answer 1

To find out how much Earl needs to invest today to retire with $320,000 at 65, given a 4% interest rate compounded semiannually, we use the present value formula for compound interest, taking into account his current age (46) and desired retirement age (65).

Step-by-step explanation:

Checkm Earl Ezekiel wishes to retire with $320,000 at the age of 65, and is currently 46 years of age. With an annual interest rate of 4%, compounded semiannually, we need to calculate the present value of the future sum to determine how much Earl needs to invest today to reach his retirement goal. This is a time value of money problem that can be solved using the present value formula for compound interest:

PV = FV / (1 + r/n)nt

Where:

• PV = Present Value
• FV = Future Value ($320,000)
• r = Annual Interest Rate (0.04)
• n = Number of times interest is compounded per year (2)
• t = Number of years until retirement (65 - 46 = 19 years)

By substituting the given values into the formula, we calculate the amount Earl should invest today.