Question

32875=P(1+20.4/5)nt

Answer 1

Is this the original problem?

Answer 2

Credit cards are one of those things that we can’t live with, and we can’t live without, it seems. They can be wonderful—We use our Hilton Honors Card, and haven’t paid to stay at a hotel in years. We learned our lesson about maintaining a balance on a credit card long ago. However, for other folks, it isn’t as easy. The formula for determining how much you actually spend over the life of a loan is A=P(1+ r/n)nt. (A little messy looking, isn’t it?) The A is the total debt accumulated, P is the principal borrowed, r is the interest rate as a decimal, t is the number of years and n is the number of times that interest is compounded per year.

I have a dear friend who, although she has learned her lesson, we hope, has, at this moment, $32, 875 in credit card debt. (She has a good job, but she also has GREAT jewelry…) Her interest is compounded daily (as it is with many credit cards) and her rate is 20.4%.
1. Use the above formula to find the total amount that she will pay back to the bank, if she is determined to repay the loan in 5 years.


this is the original problem part 1

Answer 3

\[A = P(1 + \frac{r}{n})^{nt}\]\[A = 32875(1 + \frac{0.204}{365})^{365(5)}\]Can you solve now?

Answer 4

this is where I get really confused, I know that I should solve within the parenthesis first right?

Answer 5

why did you put the interest rate at 0.204?

Answer 6

Yes. first solve 0.204/365.

Answer 7

The interest rate is put in in decimal form. What they have in the problem is percentage form.

Answer 8

oh ok thank you

Answer 9

np :)

Answer 10

ok I have that answer, but I'm not real sure how to finish the problem. I'm sorry but I am not very good in Algebra

Answer 11

ALright. 0.204/365 = ?

Answer 12

5.89

Answer 13

Not quite...0.0005589

Answer 14

how did you get that answer?

Answer 15

wouldn't you divide 0.204 by 3.65?

Answer 16

Yes. I assume that you're calculator had a symbol like E -4 or something?

Answer 17

no what I wrote was rounded off

Answer 18

Try replugging it in. It's definitely like that. If you want to double check, multiply what you get by 365 and see what you get.

Answer 19

Oh. I see what you did. You divided by 3.65. It's 365.

Answer 20

yes i did sorry about that, like I said I am not very good at Algebra

Answer 21

Alright. What do you get now?

Answer 22

5.5890419589041095890411e-4

Answer 23

\[A = 32875(1 + \frac{0.204}{365})^{365(5)}\]\[A = 32875(1 + 0.0005589)^{365(5)}\]\[A = 32875(1.0005589)^{1825}\]\[A = 32875(2.772383915)\]\[A = 91142.12\]

Answer 24

Calcmathlete, thank you so very much. I still am not real sure how you came up with that answer tho.

Answer 25

lol. Well, if you follow my steps. I first solved 0.204/365. Then I added the result to 1. Then, I multiplied 365 and 5 which were in the exponents. Then, I did what was in the parentheses to the 1825 power. Finally, I multiplied that by 32875.

Answer 26

ok, how do you do 1825 power? you have me totally lost with that

Answer 27

lol. You need a scientific calculator.

Answer 28

Basically it's like saying \[(1.0005589)^{1825}\]

Answer 29

ok that would probably be a very good idea, but i don't know how to work with one of those either. OHHHHHHHHHHHHHHHHHHHHH ok got it

Answer 30

thank you so very much! :)