Question

I don't understand how to exactly do this..
APR 19.1% compounded monthly
Grace Period 30 days
Minimum Payment 3.5% of the remaining balance or $10, whichever is higher


Patti charged $425 to her credit card last month. What is the first minimum payment she must make?

Answer 1

what is 3.5% of 425? is it bigger or smaller than 10?

Answer 2

yes, it came out to 15.75

Answer 3

then thats the minimum payment if calculated correctly :)

Answer 4

but that answer isn't one of choices

Answer 5

is 14.88?

Answer 6

yes, I put that at my answer because it was close to what I got but I don't understand how I calculated it wrong.

Answer 7

ohh. I multiplied by .35 instead of .035

Answer 8

if there had been no grace period:

425(1+.191/12) = 431.76

3.5% of 431.76 = 15.12

-----------------------------------

BUT, there is a grace period so the purchase from last month is not compounded, so just take: 3.5% of 425 = 14.88

Answer 9

Yeah, I keep forgetting to move the decimal two spots. but can you help me with on more problem?

Answer 10

on more, maybe

Answer 11

Nash uses a credit card with a 17.8% APR, compounded monthly, to pay for a cruise totaling $1,789.17. He can pay $650 per month on the card. What will the total cost of this purchase be?
Isn't that the same equation you used up there?

Answer 12

its related, but this takes on a rather new form

Answer 13

let B = 1789.17, the balance to pay off; let k = the compounding jargon (1+.178/12), and let P be the payment

M0 = B
M1 = Bk - P
M2 = Bk^2 -Pk - P
M3 = Bk^3 -Pk^2 -Pk - P
M4 = Bk^4 -Pk^3 -Pk^2 -Pk - P
....
Mn = Bk^n -P(1+k+k^2+...+k^(n-1))
^^^^^^^^^^^^^^^^^
geometrim sum in k

Mn = Bk^n -P(1-k^n)/(1-k)

they key is in solvinig this setup for n

Answer 14

let Mn = 0 be the amount when its paid off

0 = Bk^n -P(1-k^n)/(1-k)

Bk^n = P(1-k^n)/(1-k)

B(1-k)/P k^n = 1- k^n

B(1-k)/P = (1- k^n)/k^n

B(1-k)/P = 1/k^n - 1

(B(1-k)/P) + 1 = 1/k^n

1/((B(1-k)/P)+1) = k^n

ln(1/((B(1-k)/P)+1)) = n ln(k)

ln(1/((B(1-k)/P)+1))/ln(k) = n

thats was fun ....

Answer 15

ln(1/((B(1-k)/P)+1))/ln(k)

B = 1789.17
k = 1+.178/12
P = 650

ln(1/((1789.17(1-k)/650)+1))/ln(k), k = 1+.178/12

http://www.wolframalpha.com/input/?i=ln%281%2F%28%281789.17%281-k%29%2F650%29%2B1%29%29%2Fln%28k%29%2C+k+%3D+1%2B.178%2F12

id say about 3 months to pay off:

or simply 650 * n, about 1840.25

Answer 16

that was so much work, but I got it now.

Answer 17

we could of course have just gone with a couple of iterations ..

1789.17(1+.178/12) - 650

(1789.17(1+.178/12) - 650)(1+.178/12)-650

((1789.17(1+.178/12) - 650)(1+.178/12)-650)(1+.178/12); remaining balance

650+650+remaining balance

Answer 18

1840.90 if we go that route

Answer 19

just to add...this takes 30 sec with a financial calculator
depending on level of class you are taking, you may not need to know all the math behind the calculations

Answer 20

from the blank stares that i see from the accounting majors as they gaze upon their financial calculators in fear and awe ... im pretty sure those things eat your brain :)