Question

APPLY THE CONCEPTS: Present value of a single amount in the future

As it is important to know what a current investment will yield at a point in the future, it is equally important to understand what investment would be required today in order to yield a required future return. The following timeline displays what present investment is required in order to yield $8,000 three years from now, assuming annual compounding at 5%.

				Future Value: $8,000
	Year 1	Year 2	Year 3
Present Value: ?

The most straightforward method for calculating the present value of a future amount is to use the Present Value Table. By multiplying the future amount by the appropriate figure from the table, one may adequately determine the present value.

Instructions for using present value tables

+ Present Value of a Future Amount Table1 - Present Value of $1 at Compound Interest Period 5% 6% 7% 8% 9% 10% 11% 12% 1 0.952 0.943 0.935 0.926 0.917 0.909 0.901 0.893 2 0.907 0.890 0.873 0.857 0.842 0.826 0.812 0.797 3 0.864 0.840 0.816 0.794 0.772 0.751 0.731 0.712 4 0.823 0.792 0.763 0.735 0.708 0.683 0.659 0.636 5 0.784 0.747 0.713 0.681 0.650 0.621 0.593 0.567 6 0.746 0.705 0.666 0.630 0.596 0.564 0.535 0.507 7 0.711 0.665 0.623 0.583 0.547 0.513 0.482 0.452 8 0.677 0.627 0.582 0.540 0.502 0.467 0.434 0.404 9 0.645 0.592 0.544 0.500 0.460 0.424 0.391 0.361 10 0.614 0.558 0.508 0.463 0.422 0.386 0.352 0.322 11 0.585 0.527 0.475 0.429 0.388 0.350 0.317 0.287 12 0.557 0.497 0.444 0.397 0.356 0.319 0.286 0.257 13 0.530 0.469 0.415 0.368 0.326 0.290 0.258 0.229 14 0.505 0.442 0.388 0.340 0.299 0.263 0.232 0.205 15 0.481 0.417 0.362 0.315 0.275 0.239 0.209 0.183 16 0.458 0.394 0.339 0.292 0.252 0.218 0.188 0.163 17 0.436 0.371 0.317 0.270 0.231 0.198 0.170 0.146 18 0.416 0.350 0.296 0.250 0.212 0.180 0.153 0.130 19 0.396 0.331 0.277 0.232 0.194 0.164 0.138 0.116 20 0.377 0.312 0.258 0.215 0.178 0.149 0.124 0.104

Using the previous table, enter the correct factor for three periods at 5%:

Future value	x	Factor	=	Present value
$8,000	x		=	$6,912

You may want to own a home one day. If you are 20 years old and plan on buying a $500,000 house when you turn 30, how much will you have to invest today, assuming your investment yields an 8% annual return? $______________

Answer 1

Part A : How to select present value factor for 3 periods at 5  

Given : Future Value = $8000
Annual coumponding rate = 5%
Time Period = 3 years

Present value = Future value * PVF(r,t)
where r = Annual coumponding rate
and t = Time Period

$6,912 = $8,000 * PVF(5%,3)

In order to locate the present value factor (PVF) we will choose column for interest rate = 5% and row with period 3. From here we get PVF(5%,3) = 0.864

$6,912 = $8,000 * 0.864

Part B) Calculation of Present value of investment required

Future value of House = $500,000
Time period = (30 - 20)10 years
Investment yields =  8% p.a.

Present value = Future value * PVF(r,t)
where r = Annual coumponding rate
and t = Time Period

Present value = $500,000 * PVF(8%,10)

In order to locate the present value factor (PVF) we will choose column for interest rate = 8% and row with period 10. From here we get PVF(8%,10) = 0.463

Present value = $500,000 * 0.463

Present value = $231,500

Present value of investment required = $231,500