Damon won a charity raffle with a price of $7,500. If he invests the money at an interest rate of 4.3% compounded continuously,
determine the number of years, to the nearest tenth, that it will take for the money to double. (The formula for continous interest is P=Ae^rt, where A is the initial amount invested, r is the rate of interest, and t is the time invested.)
Given the initial amount is A= 7500
Also, given the rate r= 4.3% = 0.043
We need to find the time (t) needed in order for the money to double.
==> Then A = 2A = 2*7500 = 15000
==> 1500 = 7500 (e^0.043 t)
==> Divide by 7500
==> 2 = e^(0.043t)
==> Now we will rewrite using natural logarithm
==> ln 2 = ln e^(0.043t)
==> ln 2 = 0.043 t (lne)
==> ln 2 = 0.043t
==> t = (ln2)/(0.043) = 16.11
==> Then, the time needed is 16 years in order for the money to double.