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

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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) About Me  (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) About Me  (Show Source):
You can put this solution on YOUR website!

A=Pe%5E%28rt%29 Start with the continuous compounding interest formula.


2P=P%2Ae%5E%280.08%2At%29 Plug in A=2P (since we want to double our investment), and r=0.08 (note: 0.08 is the decimal equivalent of 8%).


%282P%29%2FP=e%5E%280.08%2At%29 Divide both sides by 800.


2=e%5E%280.08%2At%29 Reduce.


ln%282%29=ln%28e%5E%280.08%2At%29%29 Take the natural log of both sides.


ln%282%29=0.08%2At%2Aln%28e%29 Pull down the exponent using the identity ln%28x%5Ey%29=y%2Aln%28x%29.


ln%282%29=0.08%2At%2A1 Evaluate ln%28e%29 to get 1.


ln%282%29=0.08%2At Multiply.


0.693147=0.08%2At Evaluate ln%282%29 to get 0.693147


0.693147%2F0.08=t Divide both sides by 0.08 to isolate 't'


8.664338=t Divide 0.693147%2F0.08 to get 8.664338


t=8.664338 Rearrange the equation.


t=8.66 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) About Me  (Show Source):
You can put this solution on YOUR website!
A+=+Pe%5E%28rt%29
P is the original amount invested. The problem
wants to know how long (what t is) it takes to
make A twice this amount, so A+=+2P
2P+=+Pe%5E%28rt%29
given:
r+=+.08 (this is annual intest rate)
2P+=+Pe%5E%28.08t%29
Divide both sides by P
2+=+e%5E%28.08t%29
Take the natural log of both sides
ln%282%29+=+.08t
.69315+=+.08t
t+=+8.664 (t is the time in years)
I can find .664 years in months also
.664%2A12+=+7.9 (about 8 months)
It takes 8 years and 8 months to double money