Question

Suppose that today (year 0) your car is worth $17,000. Each year your car loses 10% of its value, but at the end of each year you add customizations to your car which increase its value by $20. Write a recurrence relation to model this situation. C(n) = if n = 0 + · C(n − 1) if n > 0

Answer 1

Explanation:

since

current value = added value by customisation + remaining value after loosing worth (100%-10% = 90%)

therefore

C(n) = $20 + 0.9*C(n-1) for n>0

C(n) = Co=$17000 for n=0

where

C(n) represents the value of the car at the end of the nth year , C(n-1) is the value at the end of the (n-1)th year and Co is the initial value