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Mathematics 11 Online
OpenStudy (anonymous):

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?

OpenStudy (amistre64):

sounds like an annuity question

OpenStudy (anonymous):

can you place it in a formula for me?

OpenStudy (amistre64):

\[D_1 = 5127(1.r) - P\] \[D_2 = (5127(1.r) - P)(1.r)-P\] \[D_3 = ((5127(1.r) - P)(1.r)-P)(1.r)-P\] ... \[D_4=5127(1.r)^4-P(1.r^0+1.r^1+1.r^2+1.r^3)\] \[D_n=5127(1.r)^n-P(1.r^0+1.r^1+1.r^2+1.r^3+...+1.r^{n-1})\] \[D_{12}=5127(1.r)^{12}-P(1.r^0+1.r^1+1.r^2+1.r^3+...+1.r^{11})\] \[0=5127(1.r)^{12}-P(1.r^0+1.r^1+1.r^2+1.r^3+...+1.r^{11})\] \[5127(1.r)^{12}=P(1.r^0+1.r^1+1.r^2+1.r^3+...+1.r^{11})\]

OpenStudy (amistre64):

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

OpenStudy (anonymous):

oo alright thanks bro

OpenStudy (amistre64):

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

OpenStudy (anonymous):

would that be 1+0.01325?

OpenStudy (amistre64):

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

OpenStudy (anonymous):

Thanks appreciate it! \^-^/

OpenStudy (amistre64):

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

OpenStudy (amistre64):

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

OpenStudy (amistre64):

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 ...

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