Depreciation

Consider a 5 year old car has a salvage value of $30k. If the straight line depreciation is $200 every month, what is the car’s original purchase cost?

Hint
The straight line depreciation formula is:
$$$D_{j}=\frac{C-S_{n}}{n}$$$
where $$C$$ is the initial cost, $$n$$ is the life span, and $$S_n$$ is the expected salvage value in year $$n$$ .
Hint 2
Convert either the depreciation to dollars per year, or the 5 years to months.
The straight line depreciation formula is:
$$$D_{j}=\frac{C-S_{n}}{n}$$$
where $$C$$ is the initial cost, $$n$$ is the life span, and $$S_n$$ is the expected salvage value in year $$n$$ .

Before solving for the initial cost, let’s convert the 5 years to months (or converting the depreciation to dollars per year works as well).
$$$5\:yr\cdot \frac{12\:months}{1\:yr}=60\:months$$$
Thus,
$$$\$200/month=\frac{C-\$30,000}{60\:months}$$$
$$$C=\$200/month(60\:months)+\$30k=\$12k+\$30k=\$42,000$$$
$42,000