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Mastery Problem: Time Value of Money

Time value of money

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 Bolden Co., a company that you regularly do business with, gives you a $19,000 note. The note is due in three years and pays simple interest of 7% annually. How much will Bolden pay you at the end of that term? Note: Enter the interest rate as a decimal. (i.e. 15% would be entered as .15)

Principal	+	( Principal	x	Rate	x	Time		)	=	Total
$fill in the blank 48e034048fa4060_1	+	($fill in the blank 48e034048fa4060_2	x	fill in the blank 48e034048fa4060_3	x	fill in the blank 48e034048fa4060_4	years	)	=	$fill in the blank 48e034048fa4060_5

Compound interest 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 Bolden Co., fearing that you wouldn't take its deal, decides instead to offer you compound interest on the same $19,000 note. How much will Bolden pay you at the end of three years if interest is compounded annually at a rate of 7%? 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	7%)	Amount of Interest)
1	$19,000	$1,330	$20,330
2	$20,330	$fill in the blank 8b4f8906cf80fda_1	$fill in the blank 8b4f8906cf80fda_2
3	$fill in the blank 8b4f8906cf80fda_3	$fill in the blank 8b4f8906cf80fda_4	$fill in the blank 8b4f8906cf80fda_5

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

MoreLessSame amount

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.

Instructionsfor 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	0.8640.7510.8460.684	=	$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? $fill in the blank cc9d8f000fe5fe2_2

APPLY THE CONCEPTS: Present value of an ordinary annuity

Many times future sums of money will not come in one payment but in a number of periodic payments. For example, imagine that you want to buy a house and know that you will have periodic mortgage payments and you need to know how much you would have to invest today in order to facilitate all of those payments into the future. This is called an ordinary annuity and it says that a certain value today at a stated interest rate is equal to a certain number of future payouts for a given amount per payment. The following timeline displays how an ordinary annuity pays out when distributed in three equal payments at an annually compounded interest rate of 5%.

		Payment: $6,000		Payment: $6,000		Payment: $6,000
	Year 1		Year 2		Year 3
Present Value:?

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	0.9090.9522.7233.791	=	$16,338

The controller at Bolden 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 Bolden purchases this type of machinery is 8%, what is the maximum amount the company should pay for the machine? $fill in the blank 340e6b051002051_2(Hint: This is basically a present value of an ordinary annuity problem as highlighted above.)

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 Bolden purchase this piece of machinery?

YesNoNot enough information

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