Kensin longs to own a Maserati. He can afford $40,000 for a car. If this year’s model sells for $135,000 and will depreciate at 10% a year, in how many years will he be able to afford this model Maserati?
135000(.9^n) = 40000
.9^n = .29629...
n log.9 = log .29629..
n = 11.5 years
How did you get .29629
by dividing 40,000 and 135,000
where is the .9 from?
To calculate the number of years Kensin will need to afford the Maserati, we'll need to consider the depreciation rate and his budget. We know this year's model sells for $135,000 and depreciates at a rate of 10% per year. Kensin can afford $40,000 for a car.
Let's break down the process step-by-step:
1. Determine the amount the Maserati depreciates each year:
The depreciation rate is 10%, so the amount depreciated each year is 10% of the Maserati's initial value, which is 10% of $135,000.
Depreciation per year = 10% of $135,000 = 0.10 * $135,000
2. Calculate the value of the Maserati after each year of depreciation:
We can subtract the depreciation amount from the initial value of $135,000 each year to get the remaining value of the Maserati.
Value after 1st year = $135,000 - (0.10 * $135,000)
Value after 2nd year = Value after 1st year - (0.10 * Value after 1st year)
Each subsequent year follows the same pattern.
3. Determine the number of years needed to reach Kensin's budget:
We need to keep subtracting the depreciation amount from the initial value until we get a value below Kensin's budget of $40,000.
The number of years it takes to reach this point is our answer.
Let's calculate:
Initial value = $135,000
Depreciation per year = 0.10 * $135,000 = $13,500
Remaining value after each year:
Year 1: $135,000 - $13,500 = $121,500
Year 2: $121,500 - $13,500 = $108,000
Year 3: $108,000 - $13,500 = $94,500
Year 4: $94,500 - $13,500 = $81,000
Year 5: $81,000 - $13,500 = $67,500
Year 6: $67,500 - $13,500 = $54,000
Year 7: $54,000 - $13,500 = $40,500
After 7 years, Kensin will be able to afford the Maserati as its value will be below his budget.