Due to both interest earnings and the fact that money put to good use should generate additional funds above and beyond the original investment, money tomorrow will be worth less than money today.

Simple interest Stone Co., a company that you regularly do business with, gives you a $16,000 note. The note is due in three years and pays simple interest of 10% annually. How much will Stone pay you at the end of that term? Note: Enter the interest rate as a decimal. (i.e. 15% would be entered as .15)

With compound interest, the interest is added to principal in the calculation of interest in future periods. This addition of interest to the principal is called compounding. This differs from simple interest, in which interest is computed based upon only the principal. The frequency with which interest is compounded per year will dictate how many interest computations are required (i.e. annually is once, semi-annually is twice, and quarterly is four times).

Imagine that Stone Co., fearing that you wouldnt take its deal, decides instead to offer you compound interest on the same $16,000 note. How much will Stone pay you at the end of three years if interest is compounded annually at a rate of 10%? If required, round your answers to the nearest cent.

	Principal	Annual Amount of	Accumulated Amount at
	Amount at	Interest (Principal at	End of Year (Principal at
	Beginning of	Beginning of Year x	Beginning of Year + Annual
Year	Year	10%)	Amount of Interest)
1	$16,000	$1,600	$17,600
2	$17,600	$_____	$_____
3	$_____	$_____	$_____

If you were given the choice to receive more or less compounding periods, which would you choose in order to maximize your monetary situation?

a. More

b. Less

c. Same amount

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

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 $200,000 house when you turn 30, how much will you have to invest today, assuming your investment yields an 8% annual return? $_____

The most simple and commonly used method of determining the present value of an ordinary annuity is to multiply the incremental payout by the appropriate rate found on the present value of an ordinary annuity table.

+ Present Value of an Ordinary Annuity

Table 2 - Present Value of an Ordinary Annuity 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	1.859	1.833	1.808	1.783	1.759	1.736	1.713	1.690
3	2.723	2.673	2.624	2.577	2.531	2.487	2.444	2.402
4	3.546	3.465	3.387	3.312	3.240	3.170	3.102	3.037
5	4.329	4.212	4.100	3.993	3.890	3.791	3.696	3.605
6	5.076	4.917	4.767	4.623	4.486	4.355	4.231	4.111
7	5.786	5.582	5.389	5.206	5.033	4.868	4.712	4.564
8	6.463	6.210	5.971	5.747	5.535	5.335	5.146	4.968
9	7.108	6.802	6.515	6.247	5.995	5.759	5.537	5.328
10	7.722	7.360	7.024	6.710	6.418	6.145	5.889	5.650
11	8.306	7.887	7.499	7.139	6.805	6.495	6.207	5.938
12	8.863	8.384	7.943	7.536	7.161	6.814	6.492	6.194
13	9.394	8.853	8.358	7.904	7.487	7.103	6.750	6.424
14	9.899	9.295	8.745	8.244	7.786	7.367	6.982	6.628
15	10.380	9.712	9.108	8.559	8.061	7.606	7.191	6.811
16	10.838	10.106	9.447	8.851	8.313	7.824	7.379	6.974
17	11.274	10.477	9.763	9.122	8.544	8.022	7.549	7.120
18	11.690	10.828	10.059	9.372	8.756	8.201	7.702	7.250
19	12.085	11.158	10.336	9.604	8.950	8.365	7.839	7.366
20	12.462	11.470	10.594	9.818	9.129	8.514	7.963	7.469

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

Periodic payment	x	Factor	=	Present value
$6,000	x	__?__	=	$16,338

The controller at Stone has determined that the company could save $8,000 per year in engineering costs by purchasing a new machine. The new machine would last 10 years and provide the aforementioned annual monetary benefit throughout its entire life. Assuming the interest rate at which Stone purchases this type of machinery is 8%, what is the maximum amount the company should pay for the machine? $____

Assume that the actual cost of the machine is $40,000. Weighing the present value of the benefits against the cost of the machine, should Stone purchase this piece of machinery?

a. Yes

b. No

c. Not enough information

X Rate Time Total Principal + ( Principal + ($ ) years) $ X II $