Multiple Choice
What is the present value of \$500 to be received in 15 years if the annual interest rate is 4.5\% compounded annually?
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10. Time Value of Money
Time Value of Money Equations
Multiple Choice
What is the present value of an ordinary annuity of \$400 invested each year for 12 years at an annual interest rate of 6%? (Round your answer to the nearest dollar.)
A
\$3,534
B
\$5,200
C
\$2,900
D
\$4,800
Verified step by step guidance1
Step 1: Understand the concept of present value of an ordinary annuity. It represents the current worth of a series of equal payments made at regular intervals, discounted at a specific interest rate.
Step 2: Use the formula for the present value of an ordinary annuity: \( PV = P \times \frac{1 - (1 + r)^{-n}}{r} \), where \( P \) is the payment amount, \( r \) is the annual interest rate (expressed as a decimal), and \( n \) is the number of periods.
Step 3: Substitute the given values into the formula: \( P = 400 \), \( r = 0.06 \), and \( n = 12 \). The formula becomes \( PV = 400 \times \frac{1 - (1 + 0.06)^{-12}}{0.06} \).
Step 4: Calculate the term \( (1 + r)^{-n} \), which is \( (1 + 0.06)^{-12} \). This represents the discount factor for 12 periods at a 6% annual interest rate.
Step 5: Compute the fraction \( \frac{1 - (1 + r)^{-n}}{r} \) and multiply it by \( P \) (the payment amount) to find the present value of the annuity. Round the result to the nearest dollar.
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