You want to purchase a new car, and you are willing to pay $19,970. If you can invest at 10% per year and you currently have $15,000, how long will it be before you have enough money to pay cash for the car

It will take 3 years to have enough money to purchase the car.

Explanation:

We can use either Compounding or Discounting Formula to determine the time it will take to make $19,970 from $15,000 when the investment rate is 10%. Lets go with the Compounding Formula:

                           Future Value = Present Value * (1 + i) ^ n

Re-arrange equation for "n" which is the Time Period:

⇒ FV / PV = (1 + i) ^ n

Taking log on both sides;

⇒ log (FV / PV) = log (1 + i) ^ n

OR log (FV / PV) = n log (1 + i)

OR n = log (FV / PV) / log (1 + i)

Simply put values now;

⇒ n = log (19,970 / 15,000) / log (1 + 10%) = log (1.33) / log (1.1) = .12 / .04

OR n = 3