Open MathNSWGitHub ↗

Depreciation

Apply the depreciation formula S=V0(1−r)nS = V_0(1 - r)^n to find salvage values, rates and initial values.

Worked examples

Finding salvage value using the depreciation formula

Straightforward

Problem

A refrigerator is purchased for $5000\$5000 and depreciates at 20%20\% per year. Find its salvage value after 33 years.

Finding the original purchase price given the salvage value

Moderate

Problem

After 44 years of depreciating at 20%20\% per year, a printer is worth $4096\$4096. Find its original purchase price.

Finding the number of years to reach a value threshold

Challenging

Problem

A car is purchased for $20 000\$20\,000 and depreciates at 10%10\% per year. Find the number of complete years until its value first falls below $13 000\$13\,000.

Practise

Q1·Straightforward
A laptop is purchased for $12 000\$12\,000 and depreciates at 10%10\% per year. Use S=V0(1−r)nS = V_0(1-r)^n to find its salvage value after 33 years.
Q2·Straightforward
A car is purchased for $25 000\$25\,000 and depreciates at 20%20\% per year. Find its salvage value after 22 years.
Q3·Straightforward
A photocopier is purchased for $6000\$6000 and depreciates at 25%25\% per year. Find its value after 22 years.
Q4·Straightforward
A motorcycle is purchased for $18 000\$18\,000 and depreciates at 10%10\% per year. Find its salvage value after 22 years.
Q5·Moderate
A camera was purchased for $10 000\$10\,000 and is worth $8100\$8100 exactly 22 years later. Find the annual depreciation rate as a percentage.
Q6·Moderate
A truck was purchased for $25 000\$25\,000 and is worth $12 800\$12\,800 after 33 years. Find the annual depreciation rate as a percentage.
Q7·Moderate
After 44 years of depreciating at 10%10\% per year, a piece of equipment is worth $6561\$6561. Find its original purchase price.
Q8·Moderate
A machine is worth $3200\$3200 after 33 years of depreciating at 20%20\% per year. Find its original purchase price.
Q9·Challenging
A car is purchased for $30 000\$30\,000 and depreciates at 15%15\% per year. By substituting consecutive integer values of nn, find the number of complete years until its value first falls below $15 000\$15\,000.
Q10·Challenging
A boat is purchased for $50 000\$50\,000 and depreciates at 20%20\% per year. By substituting consecutive integer values of nn, find the number of complete years until its value first falls below $25 000\$25\,000.
Q11·Challenging
Two cars are both purchased for $16 000\$16\,000. Car A depreciates at 10%10\% per year and Car B depreciates at 20%20\% per year. After 33 years, how many dollars more is Car A worth than Car B?
Q12·Challenging
Two machines are both purchased for $10 000\$10\,000. Machine A depreciates at 15%15\% per year and Machine B depreciates at 25%25\% per year. After 44 years, how many dollars more is Machine A worth than Machine B?