Appreciation and Depreciation

Introduction

Understanding appreciation and depreciation is helpful in various businesses because they are frequently brought up when investing in or making a significant purchase. Professionals like real estate agents, accountants, and financial managers are some examples that use appreciation and depreciation in their line of work. 

Let us say, for instance, you may determine whether a specific purchase is worth making by learning how to calculate the appreciation or depreciation value of an item or investment. You might analyze the appreciation values of two different assets to see which would make a better long-term investment because it would have a higher resale value in the future.

Let us define appreciation and depreciation, learn how to calculate them using formulas, and work through various examples in this article.

What is Appreciation?

Definition

When anything is considered to appreciate, its value rises by a specific percentage.

The difference between an investment’s previous value and its present or future value is known as appreciation. The term appreciation is the rise in the value of an investment over a specified amount of time, expressed either as a monetary sum or as a percentage.

For instance, it’s possible that the value of a real estate in your area has increased over the past 12 months. We can utilize the annual appreciation rate to anticipate the value after each year by making repeated percentage increases. For a property worth $50000, we can calculate its value after t years with 0.5% yearly appreciation. 

The table below shows the appreciation of the value of the property after t  number of years.

Years	Computation	Simplifying	Value of the Property
1	$50000 × ( 1 + 0.005 )	$50000 × ( 1 + 0.005 )	$50250
2	$50000 × ( 1 + 0.005 ) × ( 1 + 0.005 )	$50000 × ( 1 + 0.005 )2	$50501.25
3	$50000 × ( 1 + 0.005 ) × ( 1 + 0.005 ) × ( 1 + 0.005 )	$50000 × ( 1 + 0.005 )3	$500753.76
4	$50000 × ( 1 + 0.005 ) × ( 1 + 0.005 ) × ( 1 + 0.005 ) × ( 1 + 0.005 )	$50000 × ( 1 + 0.005 )4	$51007.53

Thus, the property has an estimated $51007.53 after 4 years.

Formula for Appreciation

The formula for appreciation is given by, 

FV = PV ( 1 + r )^t

where FV = the future value of an item
PV = the principal value of an item 
r = the appreciation rate expressed in decimal 
t = time

Let us say, for example, a collectible item appreciates at 3% per year. Find its estimated value in 5 years if its principal value is $70.

Substituting the following values, PV = $70, t = 5, and r = .03, into the formula, we have,

Value of the item after 5 years = $70 ( 1 + 0.03 )⁵
Value of the item after 5 years ≈ $81.15

Hence, the value of the collectible item after 5 years is approximately $81.15.

More Examples (Appreciation) 

Example 1

The property was bought in 2012 for $65000. If its value increases at 4% each year, how much is its worth in 2018?

Solution

Let us substitute the following into the formula: PV = $65000, t = 6 years, and r = 0.04.

Value of the property ( 2018 ) = PV ( 1 + r )^t 
Value of the property ( 2018 ) = $65000 ( 1 + 0.04 )⁶ ≈ $82245.74

The calculations below show the yearly appreciation value of the property.

Value of the property ( 2013 ) = \$65000 ( 1 + 0.04 ) = \$67600
Value of the property ( 2014 ) = \$67600 ( 1 + 0.04 ) = \$70304
Value of the property ( 2015 ) = \$70304 ( 1 + 0.04 ) = \$73116.16
Value of the property ( 2016 ) = \$73116.16 ( 1 + 0.04 ) = \$76040.81
Value of the property ( 2017 ) = \$76040.81 ( 1 + 0.04 ) = \$79082.44
Value of the property ( 2018 ) = \$79082.44 ( 1 + 0.04 ) ≈ \$82245.74

Therefore, the property has an estimated value of ≈ $82245.74 after 6 years.

Example 2

Using the formula for appreciation, calculate the future value of each item below.

( a ) Present Value = \$20000, Appreciation Rate = 4%, t = 3 years
( b ) Present Value = \$35500, Appreciation Rate = 2.5%, t =6 years
( c ) Present Value = \$75000, Appreciation Rate = 3.25%, t = 5 years
( d ) Present Value = \$825, Appreciation Rate = 5%, t =7 years
( e ) Present Value = \$145, Appreciation Rate = 2%, t =4 years

Solution

( a ) Present Value = $20000, Appreciation Rate = 4%, t = 3 years

FV = PV ( 1 + r )^t
Value after 3 years =  $20000 ( 1 + 0.04 )³
Value after 3 years =  $22497.28

( b ) Present Value = $35500, Appreciation Rate = 2.5%, t =6 years

FV = PV ( 1 + r )^t
Value after 6 years =  $35500 ( 1 + 0.025 )⁶
Value after 6 years ≈  $44918.83

( c ) Present Value = $75000, Appreciation Rate = 3.25%, t = 5 years

FV = PV ( 1 + r )^t
Value after 5 years =  $75000 ( 1 + 0.0325 )⁵
Value after 5 years ≈  $88005.85

( d ) Present Value = $825, Appreciation Rate = 5%, t =7 years

FV = PV ( 1 + r )^t
Value after 7 years =  $825 ( 1 + 0.05 )⁷
Value after 7 years ≈  $1160.86

( e ) Present Value = $145, Appreciation Rate = 2%, t =4 years

FV = PV ( 1 + r )^t
Value after 4 years =  $145 ( 1 + 0.02 )⁴
Value after 4 years ≈  $156.95

Example 3

The value of a house and lot appreciated by 3% this year. How much did it appreciate if it was purchased at $92000? Find the current value of the house and lot.

Solution

The principal value of the house and lot is $92000 with an appreciation rate of 3% after a year.

To calculate how much it is appreciated, we must multiply the principal value by 0.03. Hence, we have,

\$92000 × 0.03 = \$2760

Therefore, the hose and lot appreciated by $2760.

To find the current value of the house and lot, we must add \$2760 and \$92000.

Current value = \$92000 + \$2760

Current value = $94760

Hence, the current value of the house and lot is $94760.

Example 4

Julio invested $1200 in a company, and his money appreciates at 4% each year. 

( a ) How much is Julio’s investment account after 3 years? After 5 years?

( b ) How much has it been appreciated in 3 years? 5 years?

Solution

Let us use a table to show the yearly value of the investment. 

Year	Investment	Interest	Value at the end of the year
1	$1200	\$1200 × 0.04 = \$48	\$1200 + \$48 = \$1248
2	$1248	\$1248 × 0.04 = \$49.92	\$1248 + \$49.92 = \$1297.92
3	$1297.92	\$1297.92 × 0.04 = \$51.92	\$1297.92 + \$51.92 = \$1349.84
4	$1349.84	$1349.84 × 0.04 = \$53.99	\$1349.84 + \$53.99 = \$1403.83
5	$1403.83	$1403.83 × 0.04 = \$56.15	\$1403.83 + \$56.15 = \$1459.98

( a ) How much is in Julio’s investment account after 3 years? After 5 years?

The amount in the account after 3 years is \$1349.84, while the amount in the account after 5 years is \$1459.98. 

To show the same answer using the formula for appreciation, we have,

Value after 3 years = $1200 ( 1 + 0.04 )³ = \$1349.84
Value after 5 years = $1200 ( 1 + 0.04 )⁵ = \$1459.98

Hence, the investment value after 3 years is \$1349.84, while after 5 years is $1459.98.

( b ) How much has it been appreciated in 3 years? 5 years?

To calculate how much the investment has appreciated, we must subtract the initial amount from the final amount after 3 years and 5 years. Hence, we have,

\$1349.84 – \$1200 = \$149.84
\$1459.98 – \$1200 = \$259.98

Therefore, the investment has appreciated by \$149.84 after 3 years, while \$259.98 after 5 years.

What is Depreciation?

Definition

When something depreciates over time, it means that at regular intervals, its value decreases by a specific percentage.

Let us say, for instance, that a jewelry item with a current value of $1500 has a depreciation value of 4% each year. 

The table below shows the depreciation of the value of the jewelry after t  number of years.

Years	Computation	Simplifying	Value of the Property
1	$1500 × ( 1 – 0.04 )	$1500 × ( 1 – 0.04 )	$1440
2	$1500 × ( 1 – 0.04 ) × ( 1 – 0.04 )	$1500 × ( 1 – 0.04 )2	$1382.40
3	$1500 × ( 1 – 0.04 ) × ( 1 – 0.04 ) × ( 1 – 0.04 )	$1500 × ( 1 – 0.04 )3	$1327.104
4	$1500 × ( 1 – 0.04 ) × ( 1 – 0.04 ) × ( 1 – 0.04 ) – ( 1 + 0.04 )	$1500 × ( 1 – 0.04 )4	$1274.02

Therefore, the jewelry item has an estimated value of $1274.02 after 4 years. 

Formula for Depreciation

The formula for depreciation is given by, 

FV = PV ( 1 – r )^t

where FV = the future value of an item
PV = the principal value of an item 
r = the depreciation rate expressed in decimal 
t = time

Let us say, for example, a car depreciates at 3.5% per year. Find its estimated value in 6 years if its principal value is $68000.

Substituting the following values, PV = $68000, t = 6, and r = .035, into the formula, we have,

Value of the item after 6 years = $680000 ( 1 – 0.035 )⁶
Value of the item after 6 years ≈ $54912.70

Hence, the value of the collectible item after 6 years is approximately $54912.70.

More Examples (Depreciation)

Example 1

A car purchased at $48500 has a yearly depreciation rate of 3%. Find its value after 7 years.

Solution

Using the formula on depreciation, we have,

FV = PV ( 1 – r )^t
Value of the car after 7 years = $48500 ( 1 – 0.03 )⁷ 
Value of the car after 7 years ≈ $39187.17

The solution below shows the yearly value of the car.

Value of the car after 1 year = \$48500 ( 1 – 0.03 ) = \$47045
Value of the car after 2 years = \$47045 ( 1 – 0.03 ) = \$45633.65
Value of the car after 3 years = \$45633.65 ( 1 – 0.03 ) = \$44264.6405
Value of the car after 4 years = \$44264.6405 ( 1 – 0.03 ) = \$42936.70129
Value of the car after 5 years = \$42936.70129 ( 1 – 0.03 ) = \$41648.60025
Value of the car after 6 years = \$41648.60025 ( 1 – 0.03 ) = \$40399.14224
Value of the car after 7 years = \$40399.14224 ( 1 – 0.03 ) ≈ \$39187.17

Therefore, the estimated value of the car after 7 years would be \$39187.17

Example 2

Using the depreciation formula, calculate each item’s future value below.

( a ) Present Value = \$10000, Depreciation Rate = 2%, t = 8 years
( b ) Present Value = \$5500, Depreciation Rate = 3%, t =5 years
( c ) Present Value = \$12500, Depreciation Rate = 4%, t = 3 years
( d ) Present Value = \$430, Depreciation Rate = 6%, t =4 years
( e ) Present Value = \$225, Depreciation Rate = 2.5%, t =3 years
( f )  Present Value = \$730, Depreciation Rate = 4.5%, t =6 years

Solution

( a ) Present Value = $10000, Depreciation Rate = 2%, t = 8 years

FV = PV ( 1 – r  )^t
Value after 8 years =  \$10000 ( 1 – 0.02 )⁸
Value after 8 years ≈   $8507.63

( b ) Present Value = $5500, Depreciation Rate = 3%, t =5 years

FV = PV ( 1 – r  )^t
Value after 5 years =  $5500 ( 1 – 0.03 )⁵
Value after 5 years ≈  $4723.04

( c ) Present Value = $12500, Depreciation Rate = 4%, t = 3 years

FV = PV ( 1 – r  )^t
Value after 3 years =  $12500 ( 1 – 0.04 )³
Value after 3 years =  $11059.20

( d ) Present Value = $430, Depreciation Rate = 6%, t =4 years

FV = PV ( 1 – r  )^t
Value after 4 years =  $430 ( 1 – 0.06 )⁴
Value after 4 years ≈  $335.72

( e ) Present Value = $225, Depreciation Rate = 2.5%, t =3 years

FV = PV ( 1 – r  )^t
Value after 3 years =  $225 ( 1 – 0.025 )³
Value after 3 years ≈  $208.54

( f ) Present Value = $730, Depreciation Rate = 4.5%, t =6 years

FV = PV ( 1 – r  )^t
Value after 6 years =  $730 ( 1 – 0.045 )⁶
Value after 6 years ≈  $553.79

Example 3

The value of an electronic gadget depreciated 7% this year. How much did it depreciate if it was purchased at $3500? What is the current value of the gadget?

Solution

The principal value of the gadget is $3500, with a depreciation rate of 7% after a year.

To calculate how much it depreciated, we must multiply the principal value by 0.07. Hence, we have,

\$3500 × 0.07 = \$245

Therefore, the electronic gadget depreciated by $245.

To find the current value of the gadget, we must subtract \$245 from \$3500.

Current value = \$3500 – \$245
Current value = $3255

Hence, the current value of the gadget is $3255.

Example 4

A company has a total asset value of $200000 but depreciates by 7% annually. By how much have the assets declined after 3 years?

Solution

Let us first calculate the value of the asset after 3 years using PV = $200000, r = 0.07 and t = 3 years.

FV = PV ( 1 – r )^t
Value after 3 years = $200000 ( 1 – 0.07 )³
Value after 3 years = $160871.40

Hence, the value of the company’s assets after 3 years is $160871.40.

To determine how much the assets have depreciated after 3 years, we must subtract the final amount from the initial amount. So, we have,

\$200000 – \$160871.40 = \$39128.60.

Therefore, the total asset value of the company depreciated by $39128.60.

The table below shows the annual value of the assets.

Year	Investment	Depreciation	Value at the end of the year
1	$200000	\$200000 × 0.07 = \$14000	\$200000 – \$14000 = \$186000
2	$186000	\$186000 × 0.07 = \$13020	\$186000 – \$13020 = \$172980
3	$172980	\$172980 × 0.07 = \$12108.60	$172980 – \$12108.60 = \$160871.40

Summary

Appreciation

When anything is considered to appreciate, its value rises by a specific percentage.

Formula for Appreciation

FV = PV ( 1 + r )^t

where FV = the future value of an item
PV = the principal value of an item 
r = the appreciation rate expressed in decimal 
t = time

Depreciation

When something depreciates over time, it means that at regular intervals, its value decreases by a specific percentage.

Formula for Depreciation

FV = PV ( 1 – r  )^t

where FV = the future value of an item
PV = the principal value of an item 
r = the depreciation rate expressed in decimal 
t = time

Frequently Asked Questions on Appreciation and Depreciation ( FAQs)

What distinguishes appreciation from depreciation?

When an item’s worth rises, it is said to have appreciated; when it falls, it has depreciated. In real life, there are many instances of appreciation and depreciation. For example, the moment a brand-new car leaves the dealership’s area, its value drops. The value of the vehicle decreases. On the other hand, some items that are subject to appreciation in value like real estate, bonds, stocks, currency, and collectible items.

A percentage is typically used to express the pace of an item’s appreciation or depreciation. Since it is stated as an annual rate, it will take effect at the end of every calendar year.

What is the formula for calculating appreciation?

The formula for appreciation is given by, 

FV = PV ( 1 + r )^t

where FV = the future value of an item
PV = the principal value of an item 
r = the appreciation rate expressed in decimal 
t = time

What is the formula for calculating depreciation?

The formula for appreciation is given by, 

FV = PV ( 1 – r  )^t

where FV = the future value of an item
PV = the principal value of an item 
r = the depreciation rate expressed in decimal 
t = time

What is the importance of understanding appreciation and depreciation?

Understanding appreciation and depreciation is helpful across a wide range of sectors because they are frequently brought up when making a significant purchase or investment. 

The following are some examples of applications of appreciation and depreciation in real life.

• Accountants use appreciation to determine the increase in an asset’s initial value. 
• Real estate agents use depreciation to determine a property’s value decline as a result of degradation.
•  Some professionals can produce future financial plans, predict a return on investment, and decide the worth of an investment with the use of appreciation calculations in the workplace. 

What does it mean to appreciate and depreciate a currency?

In the idea of freely floating exchange rates, a currency’s appreciation and depreciation are related to the shift in its value relative to another currency. When one currency’s value rises relative to another’s value, this is known as appreciation. If one currency’s value declines relative to another’s value, this is known as depreciation. In freely floating exchange markets, the value of a currency is determined by forces of supply and demand.

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