I need help please

Question

2. After how many years will an account have $12,000 if $6,000 is deposited, and the account receives 3.8 percent interest compounded continuously?

Use the equation  

Answer 1

Continuous compounding means that you are constantly earning interest on both your initial deposit and the simple interest you earn from that.

That said, the variables in the equation mean this:

P is your initial deposit

e is 2.718

r is your interest rate

t is time, or number of years (this is what you are solving for!)

A is your final amount

Substitute:

12000 = 6000e^{(0.038 x t)}

2 = e^0.038t

Finally, use logarithms to solve. Remember that logarithms are the inverse of exponents, so the natural log (ln) is the inverse of e

ln2 = lne^0.038t

ln2 = 0.038t

t = ln2/0.038

t = 18.24 years

Hope that makes sense!