Question

Which of the following is the correct expression for finding the present value of a $500 payment two years from today if the interest rate is 6 percent?
a. $500*(1.06)^ 2
b. $500/(1.06)^ 2
c. $500 − 500(1.06)^ 2
d. $500/(1.02)^ 6

Answer 1

To find the present value of a future payment, you use the formula:

\[
PV = \frac{FV}{(1 + r)^n}
\]

where:
- \( PV \) is the present value,
- \( FV \) is the future value (the payment in the future),
- \( r \) is the interest rate (as a decimal), and
- \( n \) is the number of periods (years, in this case).

In this case, the future payment (\( FV \)) is $500, the interest rate (\( r \)) is 6 percent (or 0.06 as a decimal), and the number of years (\( n \)) is 2.

Plugging the values into the formula:

\[
PV = \frac{500}{(1 + 0.06)^2} = \frac{500}{(1.06)^2}
\]

So, the correct expression is:

**b.** \( \frac{500}{(1.06)^2} \)