Option 1: You invest $25/month at a rate of 3.25% APR compounded monthly for 30 years. Option 2: You invest $75/quarter at a rate of 4.00% APR compounded monthly for 30 years. 3) You invest $1000 at a rate of 6.25% APR compounded monthly for 30 years. 1) Which option was the least amount invested and what was the investment plan? 2) Which option yielded the highest amount at the end of the 30 years and what was the basis of the plan? 3) What is the difference in the principal invested for the highest and lowest final balances? What is the difference in the interest earned? 4) Is it better to invest more money in the beginning or the end of the 30 years?

1)

Option 3 was the least amount invested and The investment plan was single amount

2)

option 2 yielded the highest amount at the end of the 30 years, The basis of the plan is contributions are made at the beginning of the period and $75/ quarter at a rate of 4.00%

3)

Principal invested for the highest final balances = $ 17425.43

Principal invested for the lowest final balances = $ 6489.17

Difference = $ 10,936.26

Difference in the interest earned = Interest earned in 2nd option - Interest earned on 3rd option

Difference in the interest earned = 8425.43 - 5489.17

Difference in the interest earned = $ 2936.26

4)

It is better to invest more money in the beginning as it yield more ( Total Interest earned = 6209.31)

Step-by-step explanation:

Options      Contributions     Total Interest Earned                Final Balance

1                   $25/ month                6,250.50                          15,250.50

2                    $75/ quarter        8,425.43                    17,425.43

3                    $ 1000                  5,489.17                          6,489.17

Which option was the least amount invested and what was the investment plan?

Option 3 was the least amount invested and The investment plan was single amount

Which option yielded the highest amount at the end of the 30 years and what was the basis of the plan?

option 2 yielded the highest amount at the end of the 30 years, The basis of the plan is contributions are made at the beginning of the period and $75/ quarter at a rate of 4.00%

What is the difference in the principal invested for the highest and lowest final balances? What is the difference in the interest earned?

Principal invested for the highest final balances = $ 17425.43

Principal invested for the lowest final balances = $ 6489.17

Difference = $ 10,936.26

Difference in the interest earned = Interest earned in 2nd option - Interest earned on 3rd option

Difference in the interest earned = 8425.43 - 5489.17

Difference in the interest earned = $ 2936.26

Is it better to invest more money in the beginning or the end of the 30 years?

It is better to invest more money in the beginning as it yield more

The plan you would recommend for the largest return on investment (this means the most interest for the least amount invested)

Option 1  

Amount Invested = 25*12*30 = 9000

if contributions are made at the beginning of the period

Amount at the end of 30 Year = fv(rate,nper,pmt,pv,1)

rate = 3.25% compounded monthly = 3.25%/12

nper = 30 year = 30*12 = 360

pmt = 25

pv = 0

Amount at the end of 30 Year = fv(3.25%/12,360,25,0,1)

Amount at the end of 30 Year = $ 15,250.50

Total Interest earned = Amount at the end of 30 Year - Amount invested

Total Interest earned = 15250.50 - 9000

Total Interest earned = 6250.50

if contributions are made at the end of the period

Amount at the end of 30 Year = fv(rate,nper,pmt,pv,0)

rate = 3.25% compounded monthly = 3.25%/12

nper = 30 year = 30*12 = 360

pmt = 25

pv = 0

Amount at the end of 30 Year = fv(3.25%/12,360,25,0,0)

Amount at the end of 30 Year = $ 15,209.31

Total Interest earned = Amount at the end of 30 Year - Amount invested

Total Interest earned = 15209.31 - 9000

Total Interest earned = 6209.31

Option 2

Amount Invested = 75*4*30 = 9000

if contributions are made at the beginning of the period

Amount at the end of 30 Year = fv(rate,nper,pmt,pv,1)

rate = 4% compounded quarterly = 4%/4 = 1%

nper = 30 year = 30*4 = 120

pmt = 75

pv = 0

Amount at the end of 30 Year = fv(1%,120,75,0,1)

Amount at the end of 30 Year = $ 17425.43

Total Interest earned = Amount at the end of 30 Year - Amount invested

Total Interest earned = 17425.43 - 9000

Total Interest earned = 8425.43

if contributions are made at the end of the period

Amount at the end of 30 Year = fv(rate,nper,pmt,pv,0)

rate = 4% compounded quarterly = 4%/4 = 1%

nper = 30 year = 30*4 = 120

pmt = 75

pv = 0

Amount at the end of 30 Year = fv(1%,120,75,0,0)

Amount at the end of 30 Year = $ 17,252.90

Total Interest earned = Amount at the end of 30 Year - Amount invested

Total Interest earned = 17252.90 - 9000

Total Interest earned = 8252.90

Option 3

Amount Invested = 1000  

Amount at the end of 30 Year = fv(rate,nper,pmt,pv,1)

rate = 6.25% compounded monthlyy = 6.25%/12

nper = 30 year = 30*12 = 360

pmt = 0

pv = 1000

Amount at the end of 30 Year = fv(6.25%/12,360,0,1000)

Amount at the end of 30 Year = $ 6489.17

Total Interest earned = Amount at the end of 30 Year - Amount invested

Total Interest earned = 6489.17-1000

Total Interest earned = 5489.17

if farmer matt works for 8 hours a day, how many days will it take him to completely plant 12 rows of crops? each batch of cookies needs 3/4 cups of sugar.

step-by-step explanation:

hello from mrbilldoesmath!

answer:   (7x + 6y) ( 49x^2 - 42xy + 36y^2)

discussion:

in general, the factorization of a^3 + b^3 is

a^3 + b^ 3 = (a + b) ( a^2 - ab + b^2)

in our case note that 343 = 7^3 and 216 = 6^3 so the equation becomes:

343x^3 + 216y^3 = (7x)^3 + (6y)^3

if you think of a (above) as 7x and b as 6y the factorization becomes

343x^3 + 216y^3 =

((7x + 6y) (   (7x)^2 - 7x*6y + (6y)^2)   =

(7x + 6y) ( 49x^2 - 42xy + 36y^2)

you,

mrb

(a + b) (a^2 - a b + b^2)