You’re trying to save to buy a new $245,000 Ferrari. You have $50,000 today that can be invested at your bank. The bank pays 4.3 percent annual interest on its accounts. How long will it be before you have enough to buy the car?

  38 years

Explanation:

You want to find n such that the multiplier over n years gets you from 50,000 to 245,000.

  245,000 = 50,000(1 +4.3%)^n

  4.9 = 1.043^n

  log(4.9) = n·log(1.043)

  n = log(4.9)/log(1.043) ≈ 37.7

It will be about 38 years before you will have enough to afford the car at today's price.

Comment on car prices

The rate of inflation of car prices has been about 1.67% since 1953, so taking that into account, you will need much more than $245000 to buy the car. It will take more than 62 years for your bank account to catch up to the price of the car.

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