10.5: Simple Future and Present Values (Formulas)
Having done the foregoing work, it is plain to see that we can symbolically represent the mathematics using the following “language.”
Key :
The expression, or “factor,” (1 + R/p) n x p , may be used as a “multiplier” when compounding from present to future values and, in its reciprocal form, as a multiplier again when discounting from future to present value s . You will find the factors, calculated out, in interest rate tables, truncated versions of which you will find on the pages following.
“R/p” means that if the annual interest rate (R) is 12% and the number of compounding periods (p) is 12 (i.e., monthly compounding) the periodic compound rate is .12 ÷ 12 = .01. After one year, the FV would be $1 ( 1.01) 12 = $1.1268. (Notice that this compares with once – a – year compoun ding at 12%: $1 (1.12) = $1.12. The difference in Future Values is not trivial .