series help (1 Viewer)

[vanush]

The cost of a new car is $C. It's market value falls annualy in a geometric progression and is $C/10 at the end of 10 years.

Why is this solution wrong?

a= $C = C

T10 = C/10

ar^10 = C/10

Cr^10 = C/10C

r^10 = 1/10

r= 10th root of (1/10)

 

[Riviet]

T_n=ar^n-1, where T_n is the nth term.
So T₁₀=Cr^10-1
=Cr⁹

 

[vanush]

Oops, shouldve typed the solution..

Let Cost = C

Let Vn = value after n years

V1 = C * 1/r
V2 = C * (1/r)^2
.
.
V10 = C * (1/r)^10

But V10 = C10
-> C/r^10 = C/10
r^10 = 10
r = 10th root of 10
r = 1.2569 (4dp)

But for something thats depreciating shouldn't the ratio be less than 1?

 

[Riviet]

Yes, the ratio should be less than 1, and I believe your original working is correct, the answer is apparently (1/10)^1/10, which is approximately 0.794, which when raised to the power of 10 gives 1/10, and when multiplied by your original cost, C, gives C/10.