If you want to be a millionaire by age 70, and you start saving $50 a month at age 18 (with no previous savings), what expected rate of return do you need to reach your goal? A. Between 8% and 8.9% B. Between 9% and 9.9% C. Between 10% and 10.9% D. 11% or more

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  B. Between 9% and 9.9%

Step-by-step explanation:

The equation for the sum of a series of monthly payments P earning interest rate r compounded monthly for t years is given by ...

  A = P((1 +r/12)^(12t) -1)/(r/12)

The number of years in this case is ...

  70 -18 = 52

We want to find r such that ...

  1,000,000 = 50·12((1 +r/12)^(12·52) -1)/r

  10,000/6 = ((1 +r/12)^624 -1)/r

We can try some values for r to see what may work.

r = 9%

  ((1 +.09/12)^624 -1)/.09 = 1165.60 . . . not quite enough

r = 10%

  ((1 +0.10/12)^624 -1)/0.10 = 176408 . . . > 1666.67

The required interest rate will be between 9% and 10%, option B.

_____

In general, finding the exact interest rate is an iterative process. A financial calculator can do it for you. The result is near 9.86%. The graph shows a solution using a graphing calculator.

81 seats

step-by-step explanation:

if you multiply 0.65 times 125 then you get 81.5 seats. well since you can't have half of a seat you have to round down and get 81 seats in the no children zones. that leave 44 seats outside of the no children zone.

the answer is (4,3)

since the rule for r0, 90º is (-y,x) and it was already applied to form the image, all you have to do is reverse the answer using this formula.