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?

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

GPT-4o mini · Answer

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} $