Question

* Financial Algebra * [Work Is Shown]

Nancy uses a credit card with a 20.1% APR, compounded monthly, to pay for a hotel stay totaling $891.05. She can pay $350 per month on the card. What will the total cost of this purchase be?

$1,070.15

$891.05

$918.90

$1,109.95
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*MY WORK*
http://www.wolframalpha.com/input/?i=891.05*%281%2B%2820.1%25%29%2F%2812%29%29+-+350

Answer 1

I keep getting 556

Answer 2

Bo = 891.05
B1 = 891.05k - P
B2 = 891.05k^2 -Pk - P
etc ...

so lets set this up this way ... solving for n
\[0=B_ok^n-P\frac{1-k^n}{1-k}\]
\[\frac{B_o(1-k)}{P}k^n=1-k^n\]
\[\frac{B_o(1-k)}{P}=k^{-n}-1\]
\[\frac{B_o(1-k)}{P}+1=k^{-n}\]
\[\frac{B_o(1-k)+P}{P}=k^{-n}\]
\[\frac{P}{B_o(1-k)+P}=k^{n}\]
\[ln(\frac{P}{B_o(1-k)+P})=n~ ln(k)\]
\[ln(\frac{P}{B_o(1-k)+P})\div ln(k)=n\]
to determine the number of periods it takes to payoff

Answer 3

http://www.wolframalpha.com/input/?i=ln%28350%2F%28350%2B891.05%281-k%29%29%29%2Fln%28k%29%2C+k%3D1%2B.201%2F12

with any luck, it takes abt 2.623 months to pay off

Answer 4

which is to say 350*2+a alittle more

Answer 5

thats alot of trouble to find 2 months; can just do it by hand :)

891.05(1+.201/12) - 350 = 555.98

555.98(1+.201/12) - 350 = 215.29

215.29(1+.201/12) = 219

350
350
219
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919 seems about right

Answer 6

350 * 2.623 = 918.05 if we wanted to use the results of our logging for n :)

Answer 7

@amistre64 thanks again for your help !

Answer 8

youre welcome