You would like to save money to buy a new car that costs $10,000, but currently only have $8,000 and you know you won’t have any further excess savings to contribute more to it. You have available to you a fairly good savings account which pays continuously compounded 5% interest rate. Recall that:
X(t + n) = Xt e^(rn)
Using natural logarithms, solve for n to determine how long it will take for the balance of your savings to reach $10,000.