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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 ?

thanks!

TooTone
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Bob
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    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. – TooTone Feb 22 '14 at 17:00
  • How is that "fine", @Tootone? The formula is wrong...or I'm missing something basic, of course. – DonAntonio Feb 22 '14 at 17:17
  • yeah that needs to be fixed – Bob Feb 22 '14 at 17:23
  • In finance, continuous compounding has a very particular meaning: i.e. $\times e^{rt}$. See, e.g., http://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: $\lim_{n\to\infty}(1+r/n)^{nt} = e^{rt}$. – TooTone Feb 22 '14 at 17:23
  • would I get a same answer if I did it this way @TooTone – Bob Feb 22 '14 at 17:27
  • @DonAntonio had a different exponent...now I'm lost – Bob Feb 22 '14 at 17:28
  • @TooTone, that formula in your link is for "continuous" compound interest and passing to the limit. This question's case is a discrete (four years!) one... – DonAntonio Feb 22 '14 at 17:29
  • @DonAntonio Interest can be continuously compounded over a 4 year period (although not usually on a credit card!) -- and the question says compounded continuously. It depends on the context the question is asked. I have seen questions exactly like this asked where $e^{rt}$ is expected. If the OP is at school doing their first simple interest calculations, I'd go with the discrete case. If they're starting a masters in finance, I'd go with the continuous case! – TooTone Feb 22 '14 at 17:33
  • @TooTone, of course it can but for that you first have to calculate the infinitesimal Interest (or the interest in an infinitesimal period of time)...why to do things so cumbersome?! – DonAntonio Feb 22 '14 at 17:34
  • @TooTone, perhaps that's correct though in this case I think "continuously" may mean "in a continuous manner", and not "continuous" as in analysis, ans the latter would imply the calculation of the infinitesimal interest (say, divide $;19.95;$ in $;4\cdot 365;$ or something...). I don't know, in fact. – DonAntonio Feb 22 '14 at 17:36
  • @Ris yes, it would be different, but as you can see from the above discussion you ought to be clear what the question's asking. If in doubt or if you don't follow the debate, go with the answer you've accepted! – TooTone Feb 22 '14 at 17:36

2 Answers2

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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.

DonAntonio
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  • I guess I forgot 1...thank you! – Bob Feb 22 '14 at 17:08
  • 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. – DonAntonio Feb 22 '14 at 17:11
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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)

Subash Selvaraj
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  • 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. – G. H. Faust Feb 22 '14 at 17:44