Question 494471: How long does it take to double an investment of $1,000 in an amount that pays 8% annual interest rate if:
1. Interest is compounded quarterly?
2. Interest is compounded continuously?
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! How long does it take to double an investment of $1,000 in an amount that pays 8% annual interest rate if:
1. Interest is compounded quarterly?
8% annual = 2% per quarter
FV = PV*(1 + 0.02)^n
2 = (1.02)^n the amount is irrelevant, any amount will be doubled.
log(2) = n*log(1.02)
n = log(2)/log(1.02)
n =~ 35.003 quarters
You can use logs or ln, natural logs, same result
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2. Interest is compounded continuously?
FV = PV*e^rt = PV*e^0.08t
2 = e^0.08t
ln(2) = 0.08t
t = ln(2)/0.08
t =~ 8.66434 years
= 34.66 quarters
Not much difference
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