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# CSEC Mathematics: Appreciation and Depreciation

In this lesson, we will cover:

1. what appreciation and depreciation are

2. how to calculate and solve problems involving appreciation or depreciation

Appreciation is the increase of the value of something over time. Depreciation, on the other hand, is the opposite- it is the decrease of value of something over time.

You may be familiar with appreciation in terms of the value of houses or assets over time, since a house or property will appreciate the longer you own it. A car, however, depreciates over time when bough from new due to wear and tear.

Problems involving appreciation or depreciation are almost exactly the same as problems asking about compound interest. In fact, the formula for calculating it is the same as the formula we discussed in a previous post on interest.

Appreciation: V = I x (1 + r)^n

Depreciation: V = I x (1 - r)^n

V= Final value

I = Initial value

r = rate of increase or decrease of value over time

n = number of periods (years, months, weeks, depending on the question)

Example 1: A villa is purchased in 2004 for \$16.5 million. What is the value of the villa in 2009 if it appreciates in value by 7% each year?

This is a problem of appreciation, so we add the rate of change of value.

V = I x (1 + r)^n

= \$16,500,000 x (1 + 0.07)^5

= \$23,142,103.56

Example 2: A Toyota Corolla purchased in 1992 for \$1.2 million depreciated in value yearly by 1.5%. What is the car's value in 2008?

This is a problem of depreciation, so we subtract the rate of change of value.

V = I x (1 - r)^n

= \$1,200,000 x (1-0.015)^16

= \$942,238.69