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...

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.)

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hala718 | High School Teacher | (Level 1) Educator Emeritus

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P= Ae^(rt)

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.

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