If you are to receive \$20,000 in 50 years, what is its present value today assuming a discount rate of 7.5\% compounded annually?

• A. \$1,024.60
• B. \$5,000.00
• C. \$2,500.00
• D. \$7,500.00

Answer: (A)

Verified step by step guidance

1. Understand the concept of present value: Present value (PV) is the current worth of a future sum of money given a specific discount rate and time period. The formula for PV is: PV = FV / (1 + r)^n, where FV is the future value, r is the discount rate, and n is the number of periods.
2. Identify the given values: Future Value (FV) = \$20,000, Discount Rate (r) = 7.5% or 0.075, and Time Period (n) = 50 years.
3. Convert the discount rate to decimal form: Since the discount rate is given as a percentage, divide it by 100 to use it in the formula. For example, 7.5% becomes 0.075.
4. Substitute the values into the formula: Use the formula PV = FV / (1 + r)^n. Replace FV with \$20,000, r with 0.075, and n with 50.
5. Simplify the formula step by step: First, calculate (1 + r)^n, then divide FV by the result to find the present value. This will give you the present value of \$20,000 received in 50 years at a 7.5% annual discount rate.