Time Value of Money

TIME VALUE OF MONEY

INTRODUCTION

This module or note is created to provide students with step-by-step explanation and discussion on time value of money that mainly based on formulas instead of time value of money tables. The reason is so that students are able to answer all sorts of questions that involve interest rates and time period that are not available in the tables.

OUTLINE OF THE NOTE

A. Simple Interest
B. Compound Interest
1. Single Amount
• Future Value
• Present Value
• Finding the time period
• Finding interest rate
• Effective annual rate (EAR)
• Continuous compounding

2. Multiple Cash Flows
i) Annuity
• The basics
• Future Value of Annuity
• Present Value of Annuity
• Finding the number of payments of an annuity
• Finding the interest rate

ii) Mixed Cash Flows iii) Amortisation

C. Exercises

SIMPLE INTEREST

Simple interest is interest earned in each period on the original principal. The general formula for simple interest is as follows:

Simple interest, SI = P x i x t or SI = P x r x t; or simply SI = Pit or SI = Prt

where, P is the principal amount, i or r is the simple interest rate and t is the time period in years. So, if the time period is 6 months, then t = 0.5; if time period is 18 months, t = 1.5.

Example 1: Assuming a principal of $100 and a simple interest rate of 10%. Calculate the simple interest amount at the end of 5 years.

Solution: SI = $100 x 0.1 x 5 = $50

Notice that the original principal of $100 plus the simple interest of $50 equals to $150. So, P + SI = the final or accumulated amount. This is called the future value (FV) of the principal. We can use mathematical formula to find this value:

FVsimple interest = P + SI = P + Prt = P x [1 + rt]

To check our answer in example 1 above, FV (simple interest) = 100 x [1 + (0.1 x 5)] = $150

COMPOUND INTEREST

To put it simply, compound interest is interest calculated on principal plus interest received or charged from the last period. This new interest is then added to the principal plus interest amount and becomes the new principal for the calculation of interest in the next period, so on and so forth. In this sense, interest is “compounded” from one period to the other.

In simple interest earlier, interest is not compounded. Simple interest in each period is calculated based on interest multiplied by the principal amount only. The following tables illustrate the differences between the two.

Simple interest Compound interest

Year Amount Interest Year Amount Interest
1 100 10 1 100 10
2 10 2 110 11
3 10 3 121 12.1
4 10 4 133.10 13.31
5 ___ 10 5 146.41 14.641
Total 100 50 Total 161.05