Suppose that you borrow $10 comma 000 for five years at 6% toward the purchase of a car. Use PMT equals StartStartFraction Upper P left parenthesis StartFraction r Over n EndFraction right parenthesis OverOver 1 minus left parenthesis 1 plus StartFraction r Over n EndFraction right parenthesis Superscript negative nt EndEndFraction to find the monthly payments and the total interest for the loan.

The monthly payments $193.33.

The total interest for the loan $1,599.8.

Step-by-step explanation:

Given formula:

= (PMT×nt)-P

PMT= Monthly installment

P= Present value

r= Rate of interest

t= Time

n= Number of interest per year.

Here,

P=$10,000, r= 6%=0.06, t= 5 years, n=12

= (PMT×nt)-P

 =(193.33×12×5)-10,000

 =11,599.8 -10,000

 =$1,599.8

The monthly payments $193.33.

The total interest for the loan $1,599.8.

the value of v.w= -12.

step-by-step explanation:

we are given three vector r,v and w as:

r = < 5, -5, -2> ; v = < 2, -8, -8> ; w = < -2, 6, -5>

we know that r,v and w could also be represented as:

r=5i-5j-2k

v=2i-8j-8k

and w= -2i+6j-5k

where i,j and k are the unit vectors of x,y and z-axis respectively.

also we know that it has the following property:

i.i=1 ; j.j=1; k.k=1

and i.=j.i=i.k=k.i=j.k=k.j=0

i.e. when we multiply two vectors or we find it's dot product we need to only multiply the components of x coordinates with each other; y with each other and z with each other.

hence, v.w= (2i-8j- -2i+6j-5k)

                  = 2×(-2)+(-8)×(6)+(-8)×(-5)

                  = -4-48+40

                  = -12

hence, v.w= -12