What is the present value of a $600 annuity payment over 4 years if interest rates are 6 percent?
A. $475.26
B. $757.49
C. $2,079.06
D. $3,145.28
The Correct Answer and Explanation is:
To calculate the present value of an annuity, we use the formula:
[
PV = P \times \left(1 – (1 + r)^{-n}\right) / r
]
Where:
- (PV) = Present Value
- (P) = Payment per period ($600)
- (r) = Interest rate per period (6% or 0.06)
- (n) = Number of periods (4 years)
Step-by-Step Calculation:
- Identify the Variables:
- (P = 600)
- (r = 0.06)
- (n = 4)
- Calculate ( (1 + r)^{-n} ):
[
(1 + 0.06)^{-4} = (1.06)^{-4} \approx 0.7921
] - Calculate (1 – (1 + r)^{-n}):
[
1 – (1.06)^{-4} \approx 1 – 0.7921 \approx 0.2079
] - Substitute into the Present Value Formula:
[
PV = 600 \times \left(0.2079\right) / 0.06
]
[
PV = 600 \times 3.4648 \approx 2078.88
] - Final Calculation:
[
PV \approx 2079.06
]
Conclusion
Thus, the present value of a $600 annuity payment over 4 years at an interest rate of 6% is approximately $2,079.06.
The present value calculation is critical in financial decision-making as it helps assess the worth of future cash flows in today’s terms. In this case, an annuity payment is a series of equal payments made at regular intervals. By discounting future payments back to the present using the interest rate, investors can determine how much those future payments are worth today. Understanding present value is essential for comparing investment opportunities and making informed financial decisions. The formula captures the time value of money, emphasizing that a dollar received today is worth more than a dollar received in the future due to its earning potential.