Multiple Choice
Which of the following is an example of an annuity?
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10. Time Value of Money
Time Value of Money Equations
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What is the present value of $6 to be received in 3 years, discounted at an annual interest rate of 5% compounded annually?
A
$5.18
B
$6.00
C
$5.71
D
$4.95
Verified step by step guidance1
Understand the concept of present value: Present value (PV) is the current worth of a future sum of money, discounted at a specific interest rate over a given period. The formula for calculating PV is: PV = FV / (1 + r)^n, where FV is the future value, r is the annual interest rate, and n is the number of years.
Identify the given values in the problem: The future value (FV) is $6, the annual interest rate (r) is 5% (or 0.05 in decimal form), and the number of years (n) is 3.
Substitute the given values into the present value formula: PV = 6 / (1 + 0.05)^3. This sets up the calculation to determine the present value.
Simplify the denominator: Calculate (1 + 0.05)^3. This involves adding 1 to the interest rate (0.05) and then raising the result to the power of 3.
Divide the future value ($6) by the simplified denominator to find the present value. This step completes the calculation, yielding the present value of $6 discounted at 5% annually for 3 years.
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