Introduction to Accounting I

Professor Marc Smith

CHAPTER 1 MODULE 1Time Value of Money Module 1

Measurement and recording of liabilities are based on the concept of the time value of money.

Time Value of Money = Compound Interest

Time Value of Money – Module 1

Compound Interest v. Simple Interest

Simple Interest: P x R x T Earns interest on the principal invested.

Compound Interest:Earns interest on both principal invested as well as all previously earned interest.

Time Value of Money – Module 1

Four Time Value of Money Cases

1. Future Value of a Lump Sum

2. Present Value of a Lump Sum

3. Future Value of an Annuity

4. Present Value of an Annuity

Time Value of Money – Module 1

In each of the four time value of money cases, you will need to make use of table factors. These table factors can be found on the course website. Please print the table factors from the website and have them available as you work through the modules for this chapter.

If you look at the table factors, you will see that you need to know two variables in order to determine the correct factor to use. You need to know the number of periods (n) and the interest rate (i).

The n is located in the left column of each table and the i can be found in the row at the top of each table. The intersection of the i and n is the table factor you will use to solve your problem.

Time Value of Money – Module 1

?

TODAY FUTURE

In the future value of a lump sum case, we know the value of some amount today and we want to know the value at some point in the future.

• How much will today’s dollar be worth in the future?

Future Value = Present Value x Future Value Factor i,n

Time Value of Money – Module 1

Periods 5% 6% 8% 10% 4 1.2155 1.2625 1.3605 1.4641 5 1.2783 1.3382 1.4693 1.6105 8 1.4775 1.5939 1.8510 2.1436 10 1.6289 1.7909 2.1589 2.5938

Future Value = Present Value x FV Factor

Future Value = $10,000 x 1.6105

Future Value = $16,105

How much interest will Sandy earn over the five years?

$6,105($16,105 - $10,000)

10% | 5

Time Value of Money – Module 1

Question: What happened in part (a) thatmade our calculations easier?

Answer: The interest was compoundedannually.

Compounding — the frequency with which interest is added to the principal.

When interest is compounded in any way otherthan annually, you must make adjustments to theinterest rate (i) and the time period (n).

Time Value of Money – Module 1

Necessary adjustments to i & n

i ÷ # of compounds per year

n x # of compounds per year

NOTE: These adjustments must be made in alltime value of money cases.

Time Value of Money – Module 1

Periods 5% 6% 8% 10% 4 1.2155 1.2625 1.3605 1.4641 5 1.2783 1.3382 1.4693 1.6105 8 1.4775 1.5939 1.8510 2.1436 10 1.6289 1.7909 2.1589 2.5938

Future Value = Present Value x FV Factor

Future Value = $10,000 x 1.6289

Future Value = $16,289

How much interest will Sandy earn over the five year?

$6,289($16,289 - $10,000)

5% | 10

Time Value of Money – Module 1

Periods 5% 6% 8% 10% 4 1.2155 1.2625 1.3605 1.4641 5 1.2783 1.3382 1.4693 1.6105 8 1.4775 1.5939 1.8510 2.1436 10 1.6289 1.7909 2.1589 2.5938

Future value factors can be calculated as follows:

(1 + i) n

Thus, the future value factor at 5% and 10 periods:

(1 + .05) 10 = (1.05) 10 = 1.628895

In answering quiz and exam question, always use the table factors provided.

Time Value of Money – Module 1

Question: As the compounding frequency increases,what happened to the future value?

Answer: It increases.

FV Annual Compounding $16,105FV Semi-Annual Compounding $16,289

Question: Why does this happen?

Answer: The more frequent the compounding, themore interest is earned on interest thusgiving a higher future value.

Time Value of Money – Module 1