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dsp73
2 years ago
11

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
Mathematics
1 answer:
Lisa [10]2 years ago
8 0

9514 1404 393

Answer:

  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.

<u>r = 9%</u>

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

<u>r = 10%</u>

  ((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.

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3 years ago
Lucy spent a total of $6.60 on 5 apples and a package of grapes. If the package of grapes cost $2.35, how much did each apple co
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A rectangle has a length of 6 cm and a width of 3 cm. Each side is doubled in length. What is the ratio of the areas of the two
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3 years ago
Read 2 more answers
Please help with number 1
bezimeni [28]

Answer:

19.0681

Step-by-step explanation:

Given in the question that,

angle from ted to the dog = 60° with the ground

height of ted from the ground =  16ft

To find,

distance between dog and the door of ted's building

Considering the scenario make a right angle triangle:

<h3>By using pythagorus theorem:</h3>

Tan 40 = opposite / adjacent

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x = 16 / tan40

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x ≈ 19.0681 (nearest to thousand)

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