Multiple Choice
What is the present value (PV) of an annuity due with 5 payments of $2 each, assuming a discount rate of 10% per period?
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10. Time Value of Money
Time Value of Money Equations
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What is the present value of a $300 annuity payment received annually for 5 years if the interest rate is 8\% per year? (Assume payments are made at the end of each year.)
A
$1,380.00
B
$1,199.63
C
$1,469.33
D
$1,500.00
Verified step by step guidance1
Step 1: Understand the concept of present value of an annuity. The present value of an annuity is the sum of the present values of all future payments, discounted at a specific interest rate. Payments are made at the end of each year, which means this is an ordinary annuity.
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 annuity payment, \( r \) is the interest rate per period, and \( n \) is the number of periods.
Step 3: Substitute the given values into the formula. Here, \( P = 300 \), \( r = 0.08 \) (8% annual interest rate), and \( n = 5 \) (5 years). The formula becomes \( PV = 300 \times \frac{1 - (1 + 0.08)^{-5}}{0.08} \).
Step 4: Break down the calculation into smaller parts. First, calculate \( (1 + r) \), which is \( 1 + 0.08 = 1.08 \). Then calculate \( (1.08)^{-5} \), which is the reciprocal of \( (1.08)^5 \). Subtract this value from 1 to find \( 1 - (1.08)^{-5} \).
Step 5: Divide the result from Step 4 by \( r \) (0.08) and multiply by \( P \) (300) to find the present value of the annuity. This will give you the final answer.
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