Final answer:
To determine how much money you need to deposit today to have $100,000 in five years at an 8% interest rate, use the present value formula for compound interest. The calculation gives you a present value of approximately $68,058.32, so the correct answer is option c.
Step-by-step explanation:
The question asks how much money you would need to deposit today to have $100,000 in five years if the interest rate is 8 percent. This is a time value of money problem that can be solved using the present value formula for compound interest, which is:
PV = FV / (1 + r)^n
Where:
- PV = Present Value (the amount of money you need to deposit today)
- FV = Future Value (the amount of money you want to have in the future, which is $100,000 in this case)
- r = annual interest rate (8 percent or 0.08 in decimal form)
- n = number of years (5 years)
Now, let's calculate:
PV = $100,000 / (1 + 0.08)^5
PV = $100,000 / (1.08)^5
PV = $100,000 / 1.469328
PV ≈ $68,058.32
Therefore, the correct answer is c. $68,058.32. This is the amount you need to deposit today to have $100,000 in five years at an 8 percent interest rate.