SOLUTION: $40 at 4% (compounded daily) how long will it take for me to have $50?

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Question 218358: $40 at 4% (compounded daily) how long will it take for me to have $50?
Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

A=P%281%2Br%2Fn%29%5E%28nt%29 Start with the compounding interest formula.


50=40%281%2B0.04%2F365%29%5E%28365%2At%29 Plug in A=50, P=40, r=0.04 (note: 0.04 is the decimal equivalent of 4%) and n=365


50=40%281%2B0.0001096%29%5E%28365%2At%29 Divide 0.04%2F365 to get 0.0001096.


50=40%281.0001096%29%5E%28365%2At%29 Add.


%2850%29%2F%2840%29=%281.0001096%29%5E%28365%2At%29 Divide both sides by 40.


1.25=%281.0001096%29%5E%28365%2At%29 Divide 50%2F40 to get 1.25.


log%2810%2C%281.25%29%29=log%2810%2C%28%281.0001096%29%5E%28365%2At%29%29%29 Divide 50%2F40 to get 1.25.


log%2810%2C%281.25%29%29=365%2At%2Alog%2810%2C%281.0001096%29%29 Pull down the exponent.


log%2810%2C%281.25%29%29%2Flog%2810%2C%281.0001096%29%29=365%2At Divide both sides by log%2810%2C%281.0001096%29%29.


2036.0928773=365%2At Evaluate the left side with a calculator.


2036.0928773%2F365=t Divide both sides by 365 to isolate 't'.


5.5783367=t Divide.


t=5.5783367 Rearrange the equation.


t=5.58 Round to the nearest hundredth.


So it will take about 5.58 years for an initial investment of $40 to grow to $50 (compounded 365 times a year at 4%).

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
A(t) = Ao*(1+(r/n))^(nt)
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$40 at 4% (compounded daily) how long will it take for me to have $50?
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50 = 40(1+0.04/365)^(365t)
1.25 = (1+0.04/365)^(365t)
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365t*log(1+0.04/365) = log(1.25)
365t = log(1.25)/log(1+(0.04/365))
365t = 2036.3
t = 5.58 days
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Cheers,
Stan H.