SOLUTION: How long does it take your money in your savings account to double at 8% interest rate using the formula A=Pe^rt ?

Question 219496: How long does it take your money in your savings account to double at 8% interest rate using the formula A=Pe^rt ?
Found 3 solutions by solver91311, jim_thompson5910, josmiceli:
Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!

So:

If the principal has doubled, then , so:

Take the natural logarithm of both sides:

But , so:

Plug in and crank up your calculator.

John

Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!

Start with the continuous compounding interest formula.

Plug in (since we want to double our investment), and (note: 0.08 is the decimal equivalent of 8%).

Divide both sides by .

Reduce.

Take the natural log of both sides.

Pull down the exponent using the identity .

Evaluate to get .

Multiply.

Evaluate to get

Divide both sides by to isolate 't'

Divide to get

Rearrange the equation.

Round to the nearest hundredth.

So it will take about 8.66 years for an initial investment to double if it is compounded continuously at an interest rate of 8%.

Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!

is the original amount invested. The problem
wants to know how long (what is) it takes to
make twice this amount, so

given:
(this is annual intest rate)

Divide both sides by

Take the natural log of both sides

( is the time in years)
I can find years in months also
(about 8 months)
It takes 8 years and 8 months to double money

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