Question 213724
a)


{{{A=P(1+r)^t}}} Start with the given equation.



{{{5000=1000(1+0.06)^t}}} Plug in {{{P=1000}}}, {{{A=5000}}}, and {{{r=0.06}}}



{{{5000=1000(1.06)^t}}} Add



{{{5000/1000=(1.06)^t}}} Divide both sides by 1000.
 


{{{5=(1.06)^t}}} Divide



{{{log(10,(5))=log(10,(1.06^t))}}} Take the log of both sides.



{{{log(10,(5))=t*log(10,(1.06))}}} Pull down the exponent.



{{{0.69897=t*log(10,(1.06))}}} Evaluate the left side



{{{0.69897=t*0.02531}}} Evaluate the log on the right side



{{{0.69897/0.02531=t}}} Divide both sides by 0.02531.



{{{t=27.61636}}} Divide and rearrange the equation.



So it will take about 27.61 years (a little over 27 and a half years) for $1,000 to become $5,000 at an interest rate of 6%


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b)


{{{A=P(1+r)^t}}} Start with the given equation.



{{{5000=1000(1+0.12)^t}}} Plug in {{{P=1000}}}, {{{A=5000}}}, and {{{r=0.12}}}



{{{5000=1000(1.12)^t}}} Add



{{{5000/1000=(1.12)^t}}} Divide both sides by 1000.
 


{{{5=(1.12)^t}}} Divide



{{{log(10,(5))=log(10,(1.12^t))}}} Take the log of both sides.



{{{log(10,(5))=t*log(10,(1.12))}}} Pull down the exponent.



{{{0.69897=t*log(10,(1.12))}}} Evaluate the left side



{{{0.69897=t*0.04922}}} Evaluate the log on the right side



{{{0.69897/0.04922=t}}} Divide both sides by 0.04922.



{{{t=14.20093}}} Divide and rearrange the equation.



So it will take about 14.2 years (a little over 14 years) for $1,000 to become $5,000 at an interest rate of 12%