The price of a car that you want is $70,000 today. its price is expected to increase by $3300 per year. you now have $35,000 in an investment which is earning 15% per year. the number of years before you have enough to buy the car without borrowing any money is closest to:

Let n=number of years

Price of car

= 70000 * (3300n)

Value of investment

= 35000 * (1+0.15) ^n

To afford to buy the car,

Value of investment > = Price of car, or

35000 (1.15) ^n >=70000*3300n

=>

35000 (1.15) ^n / 70000 >=3300n

=>

1.15^n >=6600n,

solve using Newton's approximation.

f (n) = 1.15^n-6600n = 0

f' (n) = 0.13976 (1.15^n) - 6600

try n0=100

n1=n0-f (n0) / f' (n0)

=100-f (100) / f' (100)

=96.74

n2=n1-f (n1) / f' (n1)

=95.65

n3=n2-f (n2) / f' (n2)

=95.55

So the answer is it takes 96 years to have enough money to buy the car without borrowing.