Question

4. Suppose a Tesla's value depreciates by 12% each year. If the initial value of the Tesla was $58,000,

how many MONTHS will it take for the Tesla to be valued at 28,000. Round to the nearest whole month.

Please help, thanks!!!

Answer 1

The key word is 'depreciates'. With this information, we can use the depreciating factor
`(1-r)^n`, to find the future value of the car.

initial value = principal = p = $58,000

rate of depreciation = r = 12% ÷ 12 = 0.01

number of terms = n

future value = A = $28,000

`A = P(1-r)^n\\28000=58000(1-0.01)^n\\(14)/(29)=0.99^n\\ log_(0.99)((14)/(29))=n\\ n = (ln((14)/(29)))/(ln(0.99)) \\n = 72.5`

Therefore, it takes 73 months