Grace is planning on purchasing an Akai Professional MPC5000 drum machine for $2195. She's been pre-approved to finance her purchase with an APR of 12% over 60 months.
1) If she finances the entire purchase, what would her monthly payment be?
2) Based on the above monthly payment, how much total will she pay for the MPC5000?
3) Grace has $775 saved up and is considering paying it up front so that she'll have to borrow less. If she does, what will her monthly payment be?
4) I she decides to pay the $775 up front, how much total will she pay for the MPC5000 (don't forget to include her initial $775)?
5) Would you recommend she pay the $775 up front? Why?

1) Her monthly payment is $40.97 if she finance the total amount

2) She will pay $2458.2 for the MPC5000

3)Her monthly payment will be $26.50 if she pay her saved up money upfront

4) She will pay $2365.4 for the MPC5000

5) Yes, I recommend to pay the $775 upfront . If she pay upfront, then the amount she needs to pay for the MPC5000 is less.

Step-by-step explanation:

The cost of the drum machine is $2195

The APR is 12% over 60 months

1) the APR for 60 months is 12%

So, the APR for 1 month is

12/60 = 0.2%

The interest per month = 0.2% of 2195

= (0.2 x 2195) / 100

= 4.39

The amount to be paid per month is

= monthly amount + interest

= (2195/60) + 4.39

= 36.58 + 4.39

=$ 40.97

2) If she pays $40.97 per month then the total payment (for 60 months) for the drum machine

= 40.97 x 60

= $ 2458.2

3) the total cost is $2195 out of which she pays $775 upfront.

So she have to borrow less .

The amount to be financed is

2195- 775= $1420

The monthly interest is,

(0.2 x 1420) /100 = 2.84

Monthly she have to pay

23.66+ 2.84= $26.50

4) If she pay $775 upfront then the remaining $1420 is financed

Her monthly payment is $26.50

Then for 60 months she will pay,

26.50 x 60= $1590.4

The total amount paid for the drum machine is

775+1590.4 =$2365.4

there are lots of ways.   pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula.   the area is half the sum of the cross products of the sides.  

a(-2,6)   -2(2)-6(-5) = 26

b(-5,2)   -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3)   4(3) - (-3)(5) = 27

e(5,3)   5(3) - 3(1) = 12

f(1,3)     1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 +   18 + 27 + 12 + 12) = 57

that checks!