# The answer is that any time an equal amount is deposited in a periodic fashion (every year) into an account, you would use table 1-b.

Please watch the following videos before you start working on this assignment
You will need to perform Time Value of Money calculations to answer the last question. Please read the following section on Time Value of Money as well.
One of the critical calculations that you need to master in order to be able to project forward dollar amounts (and to complete the assignments in this class, starting with Question 3 on Assignment 1) relates to Time Value of money and Compounding. There are two types of calculations
1) Future Value of a Single Amount
2) Future Value of a Periodic set of payments
Both of these are explained in the Appendix: Time Value of Money (in the text book, end of Chapter 1 appendix). Please take some time to read through this appendix and review the examples posted. Below are two examples, illustrating the calculations for each of the two situations
1) Future Value of a Single Amount
“How much will an initial deposit of \$5,000 grow to in 15 years, if it earns 6% a year?”
To answer this question, you would use Table 1-A, on page 41 of the text. You will see that every entry in this table is an intersection of an interest rate, and a number of periods (years). The key to understanding this table is that each number in this table, represents the growth of \$1, for the specified interest rate and number of years. \$1 is invested initially and left alone (i.e. no new new money is added. Any interest earned goes back into the account and earns interest in the future as well….this “interest on interest” is what is referred to as “compound interest”). In table 1-A, if you go to the intersection of the 8% column, and 10 year row, you will find the number 2.159 (please look up this number in the table and verify that you are seeing it in the expected spot).
The way to interpret this number is as follows: “If \$1 were deposited in an account earning 8% interest per year, and if the interest were compounded (i.e. each year the interest already earned is added on to the existing amount, and the interest will be earned on an even higher amount next year), at the end of 10 years, the account would be worth \$2.159”. As soon as you understand this, it becomes obvious that you can use this knowledge to project the growth of any amount foward, once you know the interest rate and the term. Simply multiply the \$ amount that is deposited, by the factor for that interest rate and time period.
So, going back to our original question above, we go to the 6% column, and 15 year row, and we find that the factor is 2.397. Therefore, the table is telling us that \$1 would grow to \$2.397. We can extend this knowledge to calculate that \$5,000 in turn would grow to 5000 x 2.397 = \$11,985.
2) Future Value of a Periodic set of payments
If we were to deposit \$2000 into an account every year and the account were earning 7% a year, how much would we have after 10 years?
To answer this question, we need to use table 1-B on page 42. One frequent question I hear from students is: “When do I use table 1-A, and when do I use table 1-B?”. The answer is that any time an equal amount is deposited in a periodic fashion (every year) into an account, you would use table 1-B. Any time a single amount is involved (i.e. no future periodic deposits), you would use table 1-A. Note that to solve some problems, you may need to use 1-A for one part and 1-B for another part. For example, if I start with \$5000 in an account, then add \$1000 to that account every year, I would use 1-A to account for the growth of the initial \$5000 and 1-B to calculate the growth of the periodic addition of \$1000. Please keep this in mind for Assignments 1 and 2.
Going back to table 1-B, it is important to realize that every entry in that table represents how much \$1 would grow to if it was deposited every year into an account and every \$ in that account earned a certain rate of return. For example, the entry for 9% and 10 years is 15.193 (please verify this right now by going to the table). The way to interpret this number is as follows: If I were to deposit \$1 into an account, and the account were to earn 9% a year, after 10 years, I would have deposited \$10 (\$1 per year x 10), but due to compound interest, the actual balance will be \$15,193.
So the answer to the original question above would be as follows. First look up the factor for 7% and 10 years in Table 1-B. You will find that it is 13.816. Then multiply this factor by the annual amount added, \$2000. Therefore \$2000 x 13.816 = \$27,632 will be the balance in the account

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