Lesson 3: Financial Arithmetic – Depreciation and Annuities

👨🏽‍🏫 Introduction

Have you ever noticed how a brand-new car loses value quickly, or how monthly savings can grow into a big fund over time? These changes are the results of depreciation and annuities — two vital concepts in personal and business finance.

This lesson will help you understand how assets lose value, how to calculate it over time, and how regular savings (or payments) build up into a larger sum through interest.

By the end of this lesson, you will be able to:

• Explain and calculate straight-line depreciation
• Apply reducing balance depreciation formulas
• Calculate the future value of an annuity using consistent savings and interest

🧠 Key Concepts and Explanations

📉 1. Depreciation

Depreciation is the reduction in the value of a fixed asset over time. This happens due to wear and tear, age, or obsolescence.

✳️ (a) Straight-Line Depreciation

This method assumes the asset loses the same amount of value every year.

Formula:

Where:

• Cost Price = original value of the asset
• Scrap Value = value at the end of its useful life

✳️ (b) Reducing Balance Depreciation

This method applies a fixed percentage reduction to the asset’s value each year.

Formula:

Where:

• P = Original price
• r = Annual depreciation rate (decimal form)
• n = Number of years

Real-life example: Cars, electronics, and machinery are usually depreciated using the reducing balance method.

💸 2. Annuities

An annuity is a sequence of equal payments made at regular intervals. These can be monthly savings, pension payments, or insurance premiums.

In this lesson, we focus on calculating the future value (FV) of an annuity — the total amount accumulated after making regular payments and earning compound interest.

Formula:

Where:

• A = Amount paid regularly (annually)
• r = Interest rate per period (as decimal)
• n = Number of periods

Real-life example: If you save ₦5,000 per year in an account earning 10% interest, this formula helps you predict how much you’ll have after several years.

🧮 Sample Problem Walkthroughs

1. A machine costs ₦100,000 and has a scrap value of ₦10,000 after 5 years. Calculate the annual depreciation using the straight-line method.
   
   The asset depreciates by ₦18,000 every year.
2. A truck costs ₦250,000 and depreciates at 15% per year. What is its value after 3 years?
   
   The value after 3 years is ₦153,531.25
3. A student deposits ₦2,000 yearly into an education fund that earns 10% interest. Find the total amount saved after 4 years.
   
   Total savings = ₦9,282
4. Kojo pays ₦1,500 annually into a retirement account that grows by 12% per year. What will the fund be worth after 6 years?
   

✍🏽 Practice Exercises

🅰️ A. Depreciation

1. A printer was bought for ₦60,000 and is expected to have a scrap value of ₦15,000 after 5 years. Calculate the straight-line depreciation per year.
2. An equipment worth ₦80,000 depreciates by 12% annually. Find its value after 2 years using the reducing balance method.

🅱️ B. Annuities

1. A woman saves ₦3,000 annually at 8% interest. Find the total amount after 5 years.
2. Emmanuel contributes ₦10,000 every year to a cooperative fund earning 7% interest. What is the value after 6 years?

✅ Answers and Explanations

🅰️ A. Depreciation

• A1:
  
• A2:
  

🅱️ B. Annuities

• B1:
  
• B2:
  

📌 Recap

• ✅ Assets like vehicles and equipment lose value over time — this is depreciation
• ✅ Straight-line depreciation removes equal value yearly
• ✅ Reducing balance applies a % loss each year based on the remaining value
• ✅ Annuities help us calculate how regular savings grow into larger future amounts
• ✅ Both concepts are crucial for budgeting, investments, and long-term planning

💭 Reflection Prompt

Have you started saving regularly for a goal (e.g. a laptop, trip, or school fees)? Estimate how much you’ll have after 3–5 years with 10% interest using the annuity formula.