1.12.3 Depreciation

A drop in the value of an asset might be caused by a variety of different reasons, such as bad market circumstances, etc. is called depreciation.

• Machinery, equipment, and currency are some examples of assets that are likely to depreciate over time.
• It is calculated as a percentage decrease at the end of each year.
• This operates similarly to compound interest, but with a percentage reduction.
• It is calculated by

\( A=P(1- \frac{r}{100})^t \)

Where

• \( A \) is total amount
• \( P \) is principal amount
• \( r \) is percentage decrease
• \( t \) is the duration in years

Worked example:

The value, today,of one car is \( $ \ 21 000 \).

The value of this car decreases exponentially by \( 18 \)% each year.

Calculate the value of this car after \( 5 \) years.

Give your answer correct to the nearest hundred dollar.

Substitute \( P=21000 \) , \( r=18 \) and \( t=5 \) in the formula \( A=P(1- \frac{r}{100})^t \).

\( A=21000(1- \frac{18}{100}) \)

\( A=7785.536707… \)

Round to the nearest \( 100\) dollar

\( A=7800 \)

The value of this car after \( 5 \) years will be \( $7800\).

Test yourself

Question 1:

Scott invests \( $500 \) for \( 7 \) years at a rate of \( 1.5 \)% per year simple interest.

Calculate the value of his investment at the end of the \( 7 \) years.

[3]

Question 2:

Marlene invests \( $550 \) at a rate of \( 1.9 \) % per year compound interest.

Calculate the value of the investment at the end of \( 10 \) years.

[2]

Question 3:

Alan invests \( $200 \) at a rate of per year compound interest.

After \( 2 \) years the value of his investment is \( $206.46 \).

Show that \( r^2+200r-323=0 \)

[3]

Question 4:

Hans invests \( $550 \) at a rate of \( x \)% per year compound interest.

At the end of \( 10 \) years, the value of the investment is $\( 638.30 \), correct to the nearest cent.

Find the value of \( x \).

[3]

Question 5:

Edna invests \( $500 \) at a rate of \( r \)% per year compound interest.

At the end of \( 6 \) years, the value of Edna’s investment is \( $559.78 \).

Find the value of \( r \).

[3]