Upon entering college, Meagan borrowed the limit of $5000 on her credit card to help pay for expenses. The credit company charges 19.95 % interest compounded continuously. How much will Meagan owe when she graduates in four years ?

I wanted to use A(t)=A(0)e^rt, and r=19.95%, t=4, A(0)=5000

so I was thinking

A(t) = A(0)e^(rt) 
A = (5,000)e^(.1995)(4) 

Am I doing this correctly ? how do I calculate the rest? Is this is all I need ?


  • 1
    $\begingroup$ that looks fine to me. In your last line you want to have: A = (5,000)e^((.1995)(4)). I think you meant this anyway. $\endgroup$ – TooTone Feb 22 '14 at 17:00
  • $\begingroup$ How is that "fine", @Tootone? The formula is wrong...or I'm missing something basic, of course. $\endgroup$ – DonAntonio Feb 22 '14 at 17:17
  • $\begingroup$ yeah that needs to be fixed $\endgroup$ – Bob Feb 22 '14 at 17:23
  • $\begingroup$ In finance, continuous compounding has a very particular meaning: i.e. $\times e^{rt}$. See, e.g., en.wikipedia.org/wiki/Compound_interest#Continuous_compounding. As you will know, it comes from the limit of compounding over smaller and smaller number of periods $n$, something like: $\lim_{n\to\infty}(1+r/n)^{nt} = e^{rt}$. $\endgroup$ – TooTone Feb 22 '14 at 17:23
  • $\begingroup$ would I get a same answer if I did it this way @TooTone $\endgroup$ – Bob Feb 22 '14 at 17:27

How come you wrote the basis is $\;e\;$ and the exponent is $\;0.1995\;$ ?

I'd say the basis is $\;a:=1+\frac{19.95}{100}=1.1995\;$ , and the exponent is $\;4\;$ , so the ammount is

$$5,000\cdot(1.1995)^4\cong 10,350.73$$

assuming the interest is charged annually.

  • $\begingroup$ I guess I forgot 1...thank you! $\endgroup$ – Bob Feb 22 '14 at 17:08
  • $\begingroup$ That's fine, @Ris...perhaps you tried to use change of basis:$$1.1995^4=e^{4\log(1.1995)}$$ or something, but there's no real need for that and things only get messier. $\endgroup$ – DonAntonio Feb 22 '14 at 17:11
A = p(1+r/n)^nt

P = principal amount (the initial amount you borrow or deposit)

r = annual rate of interest (as a decimal)

t = number of years the amount is deposited or borrowed for.

A = amount of money accumulated after n years, including interest.

n = number of times the interest is compounded per year

A = (5,000)(1+.1995)^(4)

  • $\begingroup$ Welcome to MSE. I believe in your description of $A$ you meant to say $t$ years, not $n$ years. Additionally, the general consensus is that LaTeX should be utilised when possible. $\endgroup$ – G. H. Faust Feb 22 '14 at 17:44

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