This is the future value quadrupled in t years at an annual interest rate of 6.5% compounded daily. We need to find t.
1*(1+0.065/365)^(365t)t=4 take log on both sides, 365t(log(1+0.065/365)=log(4) => 365t=log(4)/log(1+0.065/365) t=(log(4)/log(1+0.065/365))/365 =(1.38629/.000178066)/365 =21.33 years
Check with the rule of 69, applicable to continuous compounding (an approximation to current problem) to double money, it take 69/interest rate in % years. =69/6.5 =10.62 years To double twice (quadruple), it takes twice 10.62 =21.24 years, not that far from 21.33 that we got earlier.
