Bank A pays #1%# interest per year, compounded yearly. Bank B pays #5%# interest per year, compounded monthly. How long does it take before an investment in Bank B has grown to twice as much as the same investment in Bank A?

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Answer 1 · 2017-12-17T14:27:34

Manipulated to a point where you can take over.

#2cancel(P)(1+1/100)^n = cancel(P)(1+5/1200)^(12n)#

Taking logs:

#ln(2)+nln(101/100)=12nln(1205/1200)#

Divide both sides by 12

#ln(2)/12+ (nln(101/100))/12 =nln(1205/1200)#

#ln(2)/12 =nln(1205/1200)-(nln(101/100))/12#

#ln(2)/12 =n[ln(1205/1200)-ln(101/100)/12]#

I will let you finish this off.