Posted by **ben!** on Monday, October 23, 2006 at 11:40am.

a new car depreciate by 20% in its first year. Each succeding year its depreciate by 10% assume the car is still good working condition after ten years. if the car costs $25000, calculate the value of the car after 10 years?

At 0 yrs, the value is $25000

After 1 year it is only 80% of its first value = 0.8 * 25000 = $20000

After 2 years it is worth 90% of its value at 1 yr = 0.9*20000 = $18000

After 3years it is worth 90% of its value at 2 yrs= 0.9*18000 = $16200

After 4 years it is worth 90% of its value at 3 yrs = 0.9*16200 = $14580

After 5 yrs value =$13122

After 6 yrs value =$11809.80

After 7 yrs value =$10628.82

After 8 yrs value =$ 9565.93

After 9 yrs value = $ 8609.34

After 10 yrs value = $7748.40

my question is is there an eaiser way to figure this question out like a formula I would use? and is my answer correct?

Is there an easier (or more convenient way) to calculate this? Yes, just look at how your calculations are progressing

Yr 1 Value = Price - 20% = P*.8

Yr 2 Value = P*.8*.9

Yr 3 Value = P*.8*.9*.9=P*.8*.9^{2}

Yr 4 Value = P*.8*.9^{3}

so in

Yr n Value = P*.8*.9^{n-1}

For the 10^{th} year it would be

Yr 10 Value = P*.8*.9^{9}

Are your answers correct? I'll let you answer that.