Future Value

where FV1 is the future value at the end of the first period

PV0 is the present value of the amount being saved or invested

r is the rate of interest, expressed as a decimal.

In our simple illustration,

Therefore, in our example:

and from Equation 5-2:

FV1 = PV0(1+r)

then by combining Equations 5-2 and 5-3:

This says that the future value of an amount of money in the present may be found by multiplying the amount of money by the future value interest factor equal to 1 plus the rate of interest (in decimal format) raised to the power n. The future value interest factor may be found in Table A-3 in the Appendix to this book. Note that in these tables, the rate of interest is expressed as k rather than r. If you look up the future value interest factor for 2 periods and 4%, it is 1.0816 which you would expect.

On most financial calculators, the percent interest button says "%i." To arrive at the future value of $1 for 2 years at 4%, enter 2 for N, 4 for %i (note that most calculators require that interest be entered in percent rather than decimal form without the decimal point) and 1 for PV (present value). Then hit the compute button (often "CPT") followed by FV (future value). The answer should be 1.0816.

If you are using a LOTUS spreadsheet, place the amount of the present value ($1) in a cell and move to an empty cell in which we will calculate the future value. Note that LOTUS will not allow you to use the @FV function to calculate the future value of an amount, it is used only for annuities which we will learn later in the chapter. However, we can reproduce Equation 5-5 by multiplying the present value by (1+r)n. LOTUS uses the caret ^ to represent an exponential power. Therefore, the LOTUS formula for the future value of a sum of money would be (PV)*(1+r)^n. If the present value was $1 and this amount was placed in cell B2, the formula (in any empty cell) for the future value at 4% in 2 years would be (B2)*(1.04^2) and will equal 1.0816.