Which of the following is a correct definition of the term present amount ( or present value)?

A- the total of principle and accumulated interest at the end of a loan or investment





B- an amount of money that must be deposited today at compound interest in order to provide a specific lump sum of money in the future





C- the idea that money "no" or in the present, is worth more than money in the future because is can be invested and earn interest as time goes by





D- the rate of return on investment|||B- an amount of money that must be deposited today at compound interest in order to provide a specific lump sum of money in the future|||Visualizing the Present Value (PV) Amount





Let's assume that Customer X provides your company with a promissory note for $1,000 in exchange for service your company provided. The note is due at the end of two years and it does not specify any interest. The fair market value of the note and the fair market value of the service are not known. Because of the time value of money, you know that some interest is involved in a two-year note, even though it is not stated explicitly. You estimate the interest rate by considering both the length of the loan and the credit worthiness of Customer X. If Customer X is a reputable company like Google, you know there is minimal risk and a low interest rate would be used. If, however, Customer X has a bad credit history, then a high interest rate would be used. Let's assume that you have determined 10% to be the appropriate rate for Customer X. We now know three of the four components we need: (1) the future value amount ($1,000), (2) the length of time (2 years), and (3) the interest rate (10%). With these three components, we know enough to calculate the fourth component, present value.





A timelinetime line can help us visualize what is known and what needs to be computed. The present time is noted with a "0," the end of the first period is noted with a "1," and the end of the second period is noted with a "2."





The following timeline depicts the information we know, along with the unknown component, (PV):








PV= ?? FV= $1,000








0 1 2








n = 2; i = 10%











The letter "n" refers to the length of time (in this case, two years). The letter "i" refers to the percentage interest rate used to discount the future amount (in this case, 10%). Both (n) and (i) are stated within the context of time (e.g., two years at a 12% annual interest rate).





(Later on we will give examples where (n) and (i) pertain to a half-year, a quarter of a year, or a month.)