Introduction to the present value of money

Under the concepts of the time value of money, you can determine the current, or present, value of a cash receipt or payment that will occur at some specified time in the future, given a specified rate of interest. This technique can be used to calculate the present value of a single or a series of future receipts or payments.

Lexi and Luke are walking after class between the library and the best pizzeria near campus. They're discussing Dr$.$ Phillips's latest financial management lecture, which addressed the concept of present value and the process for calculating it$.$ In anticipation of tomorrow's quiz, they've decided to review their lecture notes and the textbook materials and then practice one or two problems. Complete the missing information in the conversation that follows.

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

LEXI: According to Dr$.$ Phillips, an asset's present or $$ value is the current value of the cash flows that it will pay or receive in the future.

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

LEXI: 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.

LUKE: 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 $q,$