Multiple Choice
How is the future value of \$500 invested for one year at 6\% annual interest computed?
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10. Time Value of Money
Time Value of Money Equations
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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
Verified step by step guidance1
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.
Identify the given values: Future Value (FV) = $20,000, Discount Rate (r) = 7.5% or 0.075, and Time Period (n) = 50 years.
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.
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.
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.
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