Question 598014: How many years does it take for an investment to double in value if it is invested at 6%
if interest is compounded quarterly?
if interest is compounded continuously?
thanks
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! How many years does it take for an investment to double in value if it is invested at 6%
if interest is compounded quarterly?
if interest is compounded continuously?
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compound interest formula: A=P(1+r)^t, P=initial investment, r=interest rate per period, t=number of periods, A=amount after t periods.
For continuous compounding: A=Pe^rt
..
Quarterly compounding: A/P=2, r=.06/4=.015, t=quarters
A=P(1+r)^t
A/P=(1+.06/4)^t
A/P=(1+.015)^t
2=(1.015)^t
take log of both sides
log(2)=t*log(1.015)
t=log(2)/log(1.015)
t≈46.55 qtrs≈11.64 years
..
Continuous compounding: A/P=2, r=.06, t=years
A=Pe^rt
A/P=e^rt
2=e^rt
2=e^.06t
take log of both sides
ln2=.06t*lne
lne=1
.06t=ln2
t=ln2/.06
t≈11.55 years
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