Multiple Choice
A perpetuity has a present value (PV) of \$10,000. If the interest rate is 5\%, what is the annual payment (C) of the perpetuity?
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10. Time Value of Money
Time Value of Money Equations
Multiple Choice
If the going rate of interest is 10\% per year, what is the present value (PV) of \$1,000 to be received in 3 years? (Assume annual compounding.)
A
\$1,331.00
B
\$800.00
C
\$751.31
D
\$900.00
Verified step by step guidance1
Understand the concept of Present Value (PV): Present Value is the current worth of a future sum of money or stream of cash flows given a specified rate of return. It is calculated using the formula: PV = FV / (1 + r)^n, where FV is the future value, r is the interest rate per period, and n is the number of periods.
Identify the given values from the problem: The future value (FV) is \$1,000, the annual interest rate (r) is 10% or 0.10, and the number of years (n) is 3.
Substitute the given values into the formula: PV = 1000 / (1 + 0.10)^3. This involves adding 1 to the interest rate (0.10), raising the result to the power of 3, and then dividing the future value (\$1,000) by this calculated value.
Perform the intermediate calculations step-by-step: First, calculate (1 + 0.10) = 1.10. Then, raise 1.10 to the power of 3, which is 1.10^3. Finally, divide \$1,000 by the result of 1.10^3.
Interpret the result: The calculated present value represents the amount you would need to invest today at a 10% annual interest rate to have \$1,000 in 3 years. This demonstrates the time value of money concept.
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