A car was valued at $35 000 at the time of purchase. The reducing balance of the carwas 18% per year. The depreciating value of the car can be modelled by the recurrencerelation:𝑉0 = 35 000, 𝑉𝑛+1 = 0.92𝑉𝑛Use the recurrence relation to find the value of the car after 10 years.
Question
A car was valued at $35 000 at the time of purchase. The reducing balance of the carwas 18% per year. The depreciating value of the car can be modelled by the recurrencerelation:𝑉0 = 35 000, 𝑉𝑛+1 = 0.92𝑉𝑛Use the recurrence relation to find the value of the car after 10 years.
Solution
To find the value of the car after 10 years using the given recurrence relation, we need to apply the formula 𝑉𝑛+1 = 0.92𝑉𝑛 iteratively for 10 times. Here's how to do it:
- Start with the initial value: 𝑉0 = $35,000
- Apply the recurrence relation for the first year: 𝑉1 = 0.92 * 𝑉0 = 0.92 * 32,200
- Apply the recurrence relation for the second year: 𝑉2 = 0.92 * 𝑉1 = 0.92 * 29,624
- Continue this process until you reach the 10th year.
After doing this for 10 years, you will get the value of the car after 10 years.
Note: This process assumes that the car's value decreases by a constant rate of 18% per year.
Similar Questions
As a car ages, its value decreases. The value of a particular car with an original purchase price of $27,000 is modeled by the following function, where 𝑐 is the value at time 𝑡, in years.𝑐(𝑡)=27,000(1-0.21)𝑡What is the value of the car when it is 4 years old?The value of the car after 4 years is $What is the total depreciation amount after 5 years?After 5 years, the total depreciation amount is $
A new car is purchased for $25,000. The value of the car depreciates by 10% in the first year and 10% in the next. What is the value of the car after two years?$19,500$19,750$20,000$20,250$20,500
The price of a car depreciates in the first year by 25% in the second year by 20% in the third year by 15% and so on. The final price of the car after 3 years, if the present cost of the car is Rs. 10,00,000:Options7, 80, 0006, 90,0001, 70,0005, 10,000
A new car is purchased for 19000 dollars. The value of the car depreciates at 11.25% per year. What will the value of the car be, to the nearest cent, after 14 years?
A car's value depreciates by 20% each year. If the current value of the car is $15,000, what will be its value after one year?
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.