Question 1088272
<font color="black" face="times" size="3">We're given:
A = 25000 which is the amount we want after some time (t)
P = 10000 which is the initial deposit (aka principal)
r = 7.2% = 0.072 is the interest rate; we'll use the decimal form
n = 12 to indicate monthly compounding, or 12 times a year compounding


The goal is to find t. 


{{{A = P*(1+r/n)^(n*t)}}} Start with the compound interest formula


{{{25000 = 10000*(1+0.072/12)^(12*t)}}} Plug in all of the given values


{{{25000 = 10000*(1+0.006)^(12*t)}}}


{{{25000 = 10000*(1.006)^(12*t)}}}


{{{(25000)/(10000) = (1.006)^(12*t)}}} Divide both sides by 10000


{{{2.5 = (1.006)^(12*t)}}}


{{{(1.006)^(12*t)=2.5}}} Flip the equation


{{{log(((1.006)^(12*t)))=log((2.5))}}} Apply logs to both sides


{{{(12*t)*log((1.006))=log((2.5))}}} Use one of the log rules to pull down the exponent


{{{12*t=(log((2.5)))/(log((1.006)))}}} Divide both sides by log(1.006)


{{{12*t=(0.39794)/(0.002598)}}} Get the approximate log values


{{{12*t=153.171671}}}


{{{t=(153.171671)/(12)}}} Divide both sides by 12


{{{t=12.764306}}}


It will take about 12.764306 years. If you round to the neaest whole year, then it will take 13 years. 


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