At age 37, paul li decides to plan for his retirement at age 67. he currently has a net worth of about $45,000 including the equity in his home. he assumes that his employer will contribute $3,500 to his retirement plan at the end of each year for the next 30 years. he plans to put one-half of his money in a mutual fund containing stocks and the other one-half in a mutual fund containing bonds. estimate li’s future accumulation if his net worth grows at 5% and the mutual funds with stocks and bonds grow at 10% and 6%, respectively. (hint: calculate 3 parts and add all 3)

Paul Li decides to plan for his retirement 30 years from now. If Li’s accumulation grows 30 years from now here is the computation of his accumulation:

1.       Net worth grows at 5%

5% of $45,000 is $2,250

2,250 + 45,000= $47,250 A

2.       Mutual funds grows at 10%

10% of $52,500 is $5,250

5,250 + 52,500 = $57,750 B

3.       Bonds grows at 6%

6% of $52,500 is $3,150

3,150 + 52,500 = $55,650 C

We have to add all the three to know his accumulation 30 years from now:

A + B + C = D where d is the future accumulation

$47,250 + $57,750 + $55,650 = $160,650

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