Question 609183: how long will it take money to triple if it is invested at 5% compounded daily? 6% compounded continuously Found 2 solutions by solver91311, lwsshak3:Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website! how long will it take money to triple if it is invested at 5% compounded daily? 6% compounded continuously.
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Compound interest formula for daily compounding:
A=P(1+r)^n, P=initial investment, r=interest rate per period, n=number of periods, A=amt after n periods.
For given problem:
A=P(1+r)^n
A/P=(1+r)^n=3
(1+.05/365)^n=3
(1+.000137)^n=3
(1.000137)^n=3
take log of both sides
nlog(1.000137)=log3
n=log3/log(1.000137)
n≈8020
n=8020/365≈21.97≈22 yrs
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Compound interest formula for continuous compounding:
A=Pe^rt, P=initial investment, r=interest rate per year, t=number of years, A=amt after t years.
A/P=e^rt=3
e^.06t=3
take log of both sides
.06t*lne=ln3
lne=1
.06t=ln3
t=ln3/.06≈18.31≈18 yrs
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