GABRIELLA: So$,$ what is a present value, and why is it important to be able to calculate it$?$

DAKOTA: According to Dr$.$ Thibodeaux, an asset's present or

value is the current value of the cash flows that it will pay or

receive in the future.

GABRIELLA: Wait! Can you give me an example of when it would be appropriate to calculate a present value?

DAKOTA: Sure, but it might make more sense for you to identify such a situation. So$,$ tell me in which of the following two scenarios you would

use a present value calculation, and then explain why that is so$.$

Scenario $1$: You would like to know how much you should place on deposit to have accumulated a certain amount of money by a

specific future date.

Scenario $2$: You would like to know how much a given amount deposited today will grow into by a specific future date.

GABRIELLA: Ummm. I think

is the situation that requires the calculation of a present value.

The reason is that the amount to be placed on deposit is both

and occurs

DAKOTA: Very good! So here's your next question: How is the present value of a single amount calculated?

GABRIELLA: It can be calculated by rearranging the formula that is used in the calculation of a future value. To see this...

DAKOTA: Wait, wait, wait. Could you show me what you mean by writing it down?

Here is a sheet of paper, show me how to rearrange the future value formula to solve for a present value.

GABRIELLA: OK$,$ first, let's write down the equation used to calculate a future value $($FV$).$