Time Value of Money: Present and Future Value for Exam FM

The Fundamental Concept

The time value of money is the principle that a dollar today is worth more than a dollar in the future because today's dollar can earn interest. The accumulation function a(t) describes how one unit of money grows over time. The present value (PV) of a future payment is the amount needed today to produce that payment. If the accumulation factor from time 0 to time t is a(t), then PV = FV / a(t), where FV is the future value.

For compound interest at rate i per period, a(t) = (1 + i)^t. The present value of 1 due in n periods is v^n = 1/(1+i)^n, where v = 1/(1+i) is the discount factor.

Discount Factor and Discount Rate

The discount factor v = 1/(1+i) converts future values to present values. The discount rate d = i/(1+i) = 1 - v is the amount of interest payable at the beginning of the period per unit of ending balance. Key relationships: d = iv, i = d/(1-d), v = 1 - d, and (1-d)(1+i) = 1.

These relationships appear constantly on Exam FM. If you know any one of i, v, or d, you can find the others. For example, if d = 0.06, then v = 0.94, i = 0.06/0.94 = 0.0638.

Equations of Value

An equation of value equates the present values (or accumulated values) of all cash inflows and outflows at a chosen comparison date. Any date can be used; the answer is the same. For Exam FM, set up the equation of value, plug in what you know, and solve for the unknown (usually i or the payment amount). The key principle: two sets of cash flows are equivalent if and only if they have the same present value at any (and therefore every) comparison date.