Lesson PRESENT VALUE OF A FUTURE AMOUNT

Source code of 'PRESENT VALUE OF A FUTURE AMOUNT'

This Lesson (PRESENT VALUE OF A FUTURE AMOUNT) was created by by Theo(13342)

See BASIC FORMULAS AND ASSUMPTIONS USED IN FINANCIAL FORMULAS for an explanation of interest rates, compound interest versus simple interest, number of time periods, definition of time periods and time points, and any other topic basic to the understanding of these financial formulas and how to use them.

PRESENT VALUE OF A FUTURE AMOUNT
{{{PV(FA) = FA / ((1+i)^n) }}}
PV = Present Value
FA = Future Amount
i = Interest Rate per Time Period
n = Number of Time Periods

EXAMPLE 1

You earned $20,000 after investing for 5 years at 10% interest compounded annually.  How much money did you invest?
Formula is:

{{{PV(FA) = FA / ((1+i)^n) }}}

n = number of time periods = 5 (since the time period will be expressed in years and you are given years, you do not need to adjust this)
i = interest rate per year = 10% / 100% = .1 per year (since you are given percent interest per year, you need to convert to interest rate per year by dividing 10% by 100%)
FA = Future Amount = $20,000 (This will be entered in the formula as given after removing the $ sign and the commas)
Formula becomes:

{{{PV(FA) = 20000 / ((1.1)^5) }}} = 12418.42646 = $12418.43

EXAMPLE 2

You earned $20,000 after investing for 5 years at 10% interest compounded monthly.  How much money did you invest?
This is the same as example 1 except that interest is compounded monthly, rather than yearly.  
Formula is:

{{{PV(FA) = FA / ((1+i)^n) }}}

n = number of time periods = 5 * 12 = 60 (since you are given number of years = 5, you need to convert to months by multiplying by 12)
i = interest rate per time period in months = 10% / 100% / 12 = .008333333333 (since you are given % interest a year, you need to convert to interest rate per month by dividing by 100% and then dividing by 12)
FA = Future Amount = $20,000 (This will be entered in the formula as given after removing the $ sign and the commas)
Formula becomes:

{{{PV(FA) = 20000 / ((1.0083333333)^60) }}} = 12155.77207 = $12155.77