SOLUTION: Determine how much time is required to triple your money if interest is 5.75% and is compounded daily?
I have to use the compound interest formula: A=P(1+(r/n))^nt
Thank you, in
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Question 481976: Determine how much time is required to triple your money if interest is 5.75% and is compounded daily?
I have to use the compound interest formula: A=P(1+(r/n))^nt
Thank you, in advance!
Found 3 solutions by Alan3354, solver91311, Theo:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Determine how much time is required to triple your money if interest is 5.75% and is compounded daily?
I have to use the compound interest formula: A=P(1+(r/n))^nt
-----------------
That's the formula to use.
You didn't specify what to use for n, the number of days in a year. Use 365.
A = 3
P = 1
r = 0.0575
n = 365
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
If you want to triple your money, then 
, which means that ^{365t}\ =\ 3)
Take the natural log of both sides (actually, any base logarithm will do, but I like the natural log):
^{365t}\ =\ \ln(3))
Use:
\ =\ n\log_b(x))
\ =\ ln(3))
}{365\,\ln\left(1\ +\ \frac{.0575}{365}\right)})
All you need now is a little quality time with your calculator.
John
My calculator said it, I believe it, that settles it
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
A = 3
P = 1
r = .0575
n = 365
t is what you're solving for.
your equation becomes:
3 = 1 * (1 + (1+(.0575/365))^(365*t)
this equation becomes:
3 = (1+(.0575/365))^(365*t)
take the log of both sides of this equation to get:
log(3) = log(1+(.0575/365))^(365*t)
since log(a^b) = b*log(a), your equation becomes:
log(3) = 365*t*log(1+(.0575/365))
divide both sides of this equation by log(1+(.0575/365)) to get:
log(3)/log(1+(.0575/365)) = 365*t
divide both sides of this equation by 365 to get:
log(3)/(log(1+(.0575/365))*365) = t
solve for t using your calculator LOG function to get:
19.1078055813139
that's a little over 19 years.
plug that value into your original equation and solve.
original equation is:
3 = 1 * (1 + (.0575/365)^(365*t) which becomes:
3 = 1 * (1 + (.0575/365)^(365*19.1078055813139) which becomes:
3 = 3.00000000000001
plug that into your calculator to get:
3 = 3.00000000000001 which is close enough to say that it's right on.
the only reason it's not is because the calculator i am using goes very far out so a very tiny rounding error can actually be shown. most calculators wouldn't even show that.
note:
there are not 365 days in every year.
there are 366 days every fourth year.
you can fine tune your answer by taking 3 years at 365 days each and adding a fourth year at 366 days and then dividing the sum by 4 to get an average of 365.25 days per year.
your answer might be slightly different but not significantly so.
the actual answer would be:
log(3)/(log(1+(.0575/365.25))*365.25) = t
t = 19.1078045512825 instead of t = 19.10780455
that's a factor of 19.1078045512825/19.10780455 = 1.00000000006712 over the answer using 365 days a year.
bottom line is they're so close that it doesn't really matter, for practical purposes, whether you are using 365 days a year or 365.25 days a year.
either way, your answer is 19.1078 years if you round to the nearest 10,000th of a year.
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