To calculate the present value (PV) of a future payment, you can use the formula:
\[ PV = \frac{FV}{(1 + r)^n} \]
where:
- \( FV \) is the future value (the amount to be received in the future),
- \( r \) is the interest rate,
- \( n \) is the number of periods until the payment is received.
In this case:
- \( FV = 2000 \)
- \( r = 0.05 \) (5%)
- \( n = 2 \)
Plugging these values into the formula:
\[ PV = \frac{2000}{(1 + 0.05)^2} \] \[ PV = \frac{2000}{(1.05)^2} \] \[ PV = \frac{2000}{1.1025} \] \[ PV \approx 1818.18 \]
So the present value of a payment of $2,000 to be received two years from today at an interest rate of 5% is approximately $1,818.18.
The correct answer is O a. $1818.18.
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