10.4: Some More Simple TVM Problems

What is my Future Value under the following scenarios? (After each solution, write out the equivalent mathematical, symbolic notation.)

Scenario 1 : Assume I have $1 and I invest for one year, receiving an interest payment of .12 at the year’s end.

Scenario 2 : What if I invest for two years, receiving an interest payment of .12 at the end of each year?

$1 (1.12) (1.12) = $1 (1.12) 2 __________

Scenario 3 : What if Scenario 1 is changed to account for semi-annual compounding?

Scenario 4 : What if Scenario 2 is changed to account for semi-annual compounding?

Asking “ what is the present value of some money to be received in the future, ” is equivalent to asking how much money is needed today in order to have a certain amount later, assuming a given investment rate. In other words, for a person to have one dollar five years from now, i.e., FV, how much will s/he have to invest today at x%?

1. 1$1 (1.12) = $1.12
2. 2$1 (1.12) (1.12) = $1 (1.12) 2 = $1.2544
3. 3$1 (1 + .12/2) 2 x 1 = $1 (1.06) 2 = $1.1236
4. 4$1 (1 + .12/2) 2 x 2 = $1 (1.06) 4 = $1.2625

Notice how the above solutions display the fundamental principles of the Time Value of Money about which we already spoke . Namely, a s interest rates, the number of compounding periods per year, and time increase, the Future Value increases and the Present Value decreases.

It is very easy to make mistakes in doing these calculations. For example, remember that the compounding frequency adjustment, “p,” occurs twice in the basic TVM formula; don’t forget to make the relevant adjustments here . Be methodical and go slowly.

In the end, “eyeball” your solution. If it does not look right in terms of the TVM rules that we already know, it probably is not! It will look correct if it seems to be consistent with the above-cited characteristics of TVM.

So far, in all the foregoing examples, we have used $1 as present value. This makes it easy to learn and allows one to focus on the manner in which present and future values multiply out. In reality of course, present values would be other, greater numbers, such as $1,237,874.32. All one need do is substitute in the relevant number where heretofore we had the lonely $1 value.