Andrew M. answered • 07/16/15
Tutor
New to Wyzant
Mathematics - Algebra a Specialty / F.I.T. Grad - B.S. w/Honors
We have a compound interest problem using
A(t) = P(1+r/n)nt
A = future or final amount = $126,000
P = principal investment = $10,000
n = # times compounded annually = 1
t = # years = 10
r = interest rate as a decimal (To Be Determined)
126,000 = 10,000(1 + r/1)1(10)
126,000 = 10000(1+r)10
Divide both sides by 10,000
(1+r)10 = 12.6
We need to take the log of both sides
log(1+r)10 = log 12.6
10[log(1+r)] = log 12.6
log(1+r) = (log 12.6)/10
1+r = 10log (12.6)/10
r = 10log(12.6)/10 -1
r = 0.28836
r ≅ 28.84%
Andrew M.
Logarithms are basically "anti-exponents"
a logarithm basically asks "To what power do I raise this base to get this number?"
If an = b then logab=n
For example: log216 = 4 because 24 = 16
also, log(a) is understood to mean log base 10 of a or log10a
If any other base is used then it is placed there as I did with log216
So if no base is listed it is understood to be base 10
The only other exception is using the natural log ln a which is loge
The problem was log(1+r) = (log 12.6)/10
This means that the base '10' raised to the power of whatever was on the
other side of the equals sign had to equal (1+r)
Thus log(1+r) = (log 12.6)/10 means that 10[(log 12.6)/10 = 1+r
Please note that this was (log 12.6)/10 not log(12.6/10)
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07/16/15
Haley N.
07/16/15