Question

Karen uses her credit card to purchase a new television for $695.20. She can pay off up to $325 per month. The card has an annual rate of 17.9% compounded monthly. How much will she pay in interest?

$6.28

$16.96

$20.44

$62.16

Answer 1

Just do it one month at a time. Shall we assume payments are at the END of the month? :-)

Answer 2

yes :)

Answer 3

Let's see it.

Month 1: 695.20*(1 + 0.179/12) - 325.00 = Remaining Balance

Month 2: You tell me.

Answer 4

380.57?

Answer 5

since the period of payments are each month, and the interest rate is stated in a period of 1 year; let r = interest rate/12

m1 = B(1+r) - P
m2 = m1(1+r) - P
m3 = m2(1+r) - P
...


or written another way

m1 = B(1+r) - P
m2 = (B(1+r) - P)(1+r) - P
m3 = ((B(1+r) - P)(1+r) - P)(1+r) - P

.....


or to clean it up even more

m1 = B(1+r)^1 - P(1+r)^0
m2 = B(1+r)^2 - P( (1+r)^0 + (1+r)^1 )
m3 = B(1+r)^3 - P( (1+r)^0 + (1+r)^1 + (1+r)^2)


let 1+r = k for a clean up, the reccursion becomes

\[m_n=B(k)^n-P(1+k+k^2+k^3+k^4+...+k^{n-1})\]

Answer 6

that 1+k+k^2+k^3 .... is a geometric sum that can be state as (1-k^n)/(1-k)

\[m_n=B(k)^n-P\frac{1-k^n}{1-k}\]
if we want the nth month such that the final balance is zero
\[0=B(k)^n-P\frac{1-k^n}{1-k}\]
\[B(k)^n=P\frac{1-k^n}{1-k}\]
\[\frac{B(1-k)}{P}(k)^n=1-k^n\]
\[\frac{B(1-k)}{P}=k^{-n}-1\]
\[\frac{B(1-k)+P}{P}=k^{-n}\]
\[\log_k(\frac{P}{B(1-k)+P})=n\]
that looks like fun

Answer 7

the good news is that it looks like its only gonna take about 2.19 months to pay off

Answer 8

she ends up paying
718.12 for the thing
-695.20
--------
22.92 which prolly has some error in it, but is close enough :)

Answer 9

that's really confusing 0_o

Answer 10

lol, when i cant remember a formula, i tend to have to reinvent it

Answer 11

what formulas do they give you in your material to be able to work with this?

Answer 12

Month 1: 695.20*(1 + 0.179/12) - 325.00 = 380.57

Month 2: 380.57*(1 + 0.179/12) - 325.00 = 61.25

Month 3: 61.25*(1 + 0.179/12) - 62.16 = 0.00

It does not take 2.9 months. It takes 3 months.

Total Paid: 325.00 + 325.00 + 62.16 = 712.16
Total Interest Paid: 712.16 - 695.20 = 16.96

Answer 13

yeah, i got to 2.19 and forgot to round the months to 3 :)