Question

a debt of$5,127 on a credit card, with a 15.9 interest rate and compounded monhtly. What should I pay every month to pay it off in 12 months?

Answer 1

sounds like an annuity question

Answer 2

can you place it in a formula for me?

Answer 3

\[D_1 = 5127(1.r) - P\]
\[D_2 = (5127(1.r) - P)(1.r)-P\]
\[D_3 = ((5127(1.r) - P)(1.r)-P)(1.r)-P\]
...
\[D_4=5127(1.r)^4-P(1.r^0+1.r^1+1.r^2+1.r^3)\]


\[D_n=5127(1.r)^n-P(1.r^0+1.r^1+1.r^2+1.r^3+...+1.r^{n-1})\]
\[D_{12}=5127(1.r)^{12}-P(1.r^0+1.r^1+1.r^2+1.r^3+...+1.r^{11})\]
\[0=5127(1.r)^{12}-P(1.r^0+1.r^1+1.r^2+1.r^3+...+1.r^{11})\]
\[5127(1.r)^{12}=P(1.r^0+1.r^1+1.r^2+1.r^3+...+1.r^{11})\]

Answer 4

in a formula? i always have to rebuild the formula .... since i can never quite recall it

Answer 5

oo alright thanks bro

Answer 6

now we are left with a geometric sum ... such that\[S=\frac{1-1.r^{12}}{1-1.r}\]
\[5127(1.r)^{12}=P*S\]
\[5127(1.r)^{12}/S=P\]

and that r is equal to (.159/12) = .01325

Answer 7

would that be 1+0.01325?

Answer 8

yep, it was just easier to keep track of thru the processs as an r for me :) sooo

\[P=5127\frac{(1.01325)^{12}(1-1.01325)}{(1-1.01325)^{12}}\]

should do it

Answer 9

Thanks appreciate it! \^-^/

Answer 10

hmm, the wolf seems to suggest an error along the way

Answer 11

its prolly in my recollection of the sum of a geoSeq. gonna have to long hand it to remember some stuff :)

Answer 12

S = 1.r0+1.r1+1.r2+1.r3+...+1.r11
- 1.r S = -1.r1 -1.r2-1.r3 -... -1.r11-1.r12
--------------------------------------------
1-1.r S = 1 +0 +0 +0 ... +0 - 1.r12

S = (1-1.r12)/(1-1.r) .... thats right, i just placed the wrong exponent in the wolf ...

Answer 13

thats better: http://www.wolframalpha.com/input/?i=5127*1.01325%5E12%281-1.01325%29%2F%281-1.01325%5E12%29