Question

Zachary purchased a computer for ​1,140 on a payment plan.
Eight months after he purchased the​ computer, his balance was 320.
Nine months after he purchased the​ computer, his balance was ​$185. What is an equation that models the balance y after x​ months?
Can you please explain I don't know how to solve it!

Answer 1

You have two unknowns,
1. the monthly payment , let it be p
2. the rate of interest , let i be the monthly rate

after 8 months: balance = 1140(1+i)^8 - p( (1+i)^8 - 1)/i = 320
after 9 months: balance = 1140(1+i)^9 - p( (1+i)^9 - 1)/i = 185

we also know that 320(1+i) - p = 185
p = 320 + 320i - 185
p = 135 +320i

sub that into 1140(1+i)^8 - p( (1+i)^8 - 1)/i = 320
<b>1140(1+i)^8 - (135 +320i)( (1+i)^8 - 1)/i = 320</b>

Not even trying to solve this by some algebraic method and I will send it directly to Wolfram. (had to change the i to x, Wolfram read i as the imaginary number)
https://www.wolframalpha.com/input/?i=1140%281%2Bx%29%5E8+-+%28135+%2B320x%29%28+%281%2Bx%29%5E8+-+1%29%2Fx+%3D+320
got i = .0656167
p = $156.00

Made up a little Excel routine to show my answer is correct, (I am off by 3 cents)

time payment interest outstanding balance

0 $1,140.00
1 $156 $74.80 $1,058.80
2 $156 $69.48 $972.28
3 $156 $63.80 $880.08
4 $156 $57.75 $781.82
5 $156 $51.30 $677.12
6 $156 $44.43 $565.55
7 $156 $37.11 $446.66
8 $156 $29.31 $319.97
9 $156 $21.00 $184.97
10 $156 $12.14 $41.11

Unfortunately, in our format on Jishka it is hard to line up columns

my formula is
<b>y = 1140(1.0656167)^x -156(1.0656167)^x - 1)/.0656167</b>

testing it for x = 6 gave me y = 565.55 , as confirmed in my Excel routine