Time value of money - Simple and compound interest, discount...

Learning Outcomes

After completing this article, you will be able to calculate and compare simple and compound interest, apply discounting to determine present values, and explain the importance of these calculations in business financial decisions. You will also recognize key differences and be able to answer typical exam questions about the time value of money for ACCA FFM.

ACCA Foundations in Financial Management (FFM) Syllabus

For ACCA Foundations in Financial Management (FFM), you are required to understand how the time value of money affects financial decisions and calculations. In preparation for the exam, focus your revision on:

• Explaining the concept of time value of money and its significance in financial management
• Calculating simple interest for short-term finance arrangements
• Calculating compound interest over multiple periods
• Applying discounting techniques to calculate present values of future cash flows
• Comparing results of simple vs compound interest and understanding their respective uses
• Using discount and interest factors from tables for forecasting and evaluation

Test Your Knowledge

Attempt these questions before reading this article. If you find some difficult or cannot remember the answers, remember to look more closely at that area during your revision.

1. Which type of interest calculation accounts for interest earned on accumulated interest:
   1. Simple interest
   2. Flat-rate interest
   3. Compound interest
   4. Nominal interest

2. An investor places $2,000 in an account earning 5% compound interest annually. What is the total balance after 3 years, to the nearest dollar (ignore taxes)?

3. Define 'present value' in the context of discounting cash flows.

4. True or false? The total amount of interest earned using simple interest will always be less than that calculated using compound interest, for the same rate and time period.

Introduction

Money received or paid today is not equivalent to the same amount received or paid in the future. To reflect this, financial decisions must account for the time value of money. This article explains how interest is applied to money over time—either using simple or compound methods—and how discounting allows us to convert future sums into present values for better decision-making.

Key Term: time value of money
The principle that money available now is worth more than the same amount in the future, due to its earning capacity.

Simple Interest

Simple interest provides a straightforward way to calculate earnings on borrowed or invested funds over time. The calculation uses only the original principal amount; interest is not earned on interest itself.

Formula (Simple Interest)

Simple interest (SI) = Principal × Rate × Time
Where:

• Principal is the original amount invested or borrowed
• Rate is the annual interest rate (as a decimal)
• Time is the number of years

Key Term: simple interest
Interest calculated only on the original principal for each time period, not on previously accumulated interest.

Worked Example 1.1

A company borrows $10,000 at a simple interest rate of 4% per annum for 3 years. How much interest must the company pay, and what is the total repayment?

Answer:
Interest = $10,000 × 0.04 × 3 = $1,200.
Total repayment = $10,000 (principal) + $1,200 (interest) = $11,200.

Compound Interest

Unlike simple interest, compound interest calculates interest on both the initial principal and any previously earned interest. This means the amount grows at an increasing rate over time.

Formula (Compound Interest)

Compound amount (CA) = Principal × (1 + Rate)ⁿ
Where:

• n is the number of compounding periods

Compound interest (CI) = Compound amount – Principal

Key Term: compound interest
Interest calculated on the original principal plus all accumulated interest from previous periods.

Worked Example 1.2

LongCo invests $4,000 at a compound rate of 6% per year for 4 years. What is the value of the investment after 4 years? (Round to the nearest dollar.)

Answer:
CA = $4,000 × (1 + 0.06)^4
= $4,000 × 1.2625 ≈ $5,050
Compound interest = $5,050 – $4,000 = $1,050

Comparing Simple and Compound Interest

The difference between the two methods becomes more pronounced over longer periods or at higher rates. Compound interest will always result in a higher return if the same principal, rate, and term are used.

Worked Example 1.3

Suppose $2,500 is invested for 5 years at an annual rate of 5%. What is the difference between interest earned under simple and compound methods?

Answer:
Simple: $2,500 × 0.05 × 5 = $625; Simple total = $3,125
Compound:
$2,500 × (1 + 0.05)^5 = $2,500 × 1.2763 ≈ $3,191
Compound interest = $691
Difference: $691 – $625 = $66

Exam Warning

Questions may require you to compare simple and compound interest results for the same scenario. Be sure to apply the correct formula—using the wrong method will lose marks.

Discounting and Present Value

When evaluating future amounts, it is important to determine their equivalent value in today's terms. This is known as discounting—a fundamental technique in financial management.

Key Term: discounting
Reducing a future sum of money to its present value by removing the interest that would be earned over the period.

Key Term: present value
The amount that must be invested today at a specified interest rate to equal a future sum of money.

Present value (PV) uses the reverse of compound interest:

PV = Future Value × (1 + Rate)⁻ⁿ

Where:

• Future Value is the sum to be received in the future
• Rate is the discount rate per period
• n is the number of periods

Worked Example 1.4

Vela Ltd expects to receive $8,000 in 3 years. If the relevant annual discount rate is 5%, what is the present value?

Answer:
PV = $8,000 × (1 + 0.05)^-3
(1 + 0.05)^3 = 1.1576; Inverse ≈ 0.8638
PV = $8,000 × 0.8638 = $6,910

Using Discount or Present Value Tables

For ease, present value and discount factor tables may be provided. For example, the 3-year, 5% factor above can be directly read as 0.8638.

Application in Business Decisions

The time value of money is used in areas such as:

• Loan and investment analysis
• Evaluating cash flows from projects (e.g., NPV calculations)
• Deciding between payment or receipt timings

Revision Tip

Practice applying both interest and discounting methods to realistic business scenarios. Be familiar with interpreting table factors and formulas.

Summary

Interest earned on money depends on how and when it is calculated. Simple interest applies only to the original amount, whereas compound interest includes accumulated interest, resulting in greater earnings over time. Discounting enables financial managers to compare the current worth of future payments or receipts, supporting accurate and fair decision-making.

Key Point Checklist

This article has covered the following key knowledge points:

• Explain the time value of money and its importance in finance
• Calculate simple interest and total payment or receipts
• Calculate compound interest and compare it to simple interest
• Determine present values using discounting techniques
• Use interest and discount factors appropriately in scenarios
• Recognize which method is appropriate to different decision types

Key Terms and Concepts

• time value of money
• simple interest
• compound interest
• discounting
• present value