Question 956874
if $8000 is invested in a 2.5% account for 10 years compounded continuously how long would it take for the account to double?
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Formula for continuous compounding: A=Pe^rt, P=initial investment, r=interest rate, A=amt after t-years.
For given problem:
P=8000
r=.025
t=10 yrs
A=8000e^(.025*10)
A=8000e^(.25)
A≈10272
Amount in account after 10 years≈$10,272
..
doubling the acct:
A/P=2=e^.025t
take log of both sides
.025t*lne=ln2
lne=1
.025t=ln2
t=ln2/.025
t≈28 
how long would it take for the account to double? 28 yrs