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natita [175]
2 years ago
14

A family starts an education fund for their son Patrick when he is 8 years old, investing $500 on his eighth birthday, and incre

asing the yearly investment by $500 per year until Patrick is 21 years old. The fund pays 6% annual interest. What is the fund’s future worth after the deposit when Patrick is 21?
Business
1 answer:
Bas_tet [7]2 years ago
3 0

Answer:

The fund’s future worth after the deposit when Patrick is 21 is $8,713,691.01.

Explanation:

This can be calculated using the for formula for calculating the future value of a growing annuity as follows:

FW = C * (((1 + r)^n - (1 + g)^n) / (r - g))

Where;

FW = future worth or future value = ?

C = first deposit = $500

r = annual interest rate = 6%, or 0.06

g = growth rate of investment = Yearly investment increase / First deposit = $500 / $500 = 1

n = number of years = 21 - 8 + 1 = 14

Substituting all the values into equation (1), we have:

FW = $500 * (((1 + 0.06)^14 - (1 + 1)^14) / (0.06 - 1))

FW = $500 * ((1.06^14 - 2^14) / - 0.94)

FW = $500 * (2.26090395575443 - 16,384) / -0.94)

FW = $500 * (-16,381.7390960442 / -0.94)

FW = $500 * 17,427.3820170683

FW = $8,713,691.00853415

Rounding to 2 decimal places, we have:

FW = $8,713,691.01

Therefore, the fund’s future worth after the deposit when Patrick is 21 is $8,713,691.01.

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2 years ago
Lindon Company is the exclusive distributor for an automotive product that sells for $34.00 per unit and has a CM ratio of 30%.
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Answer:

1. $23.80

2. Break even Point (units) = 19,000 units and Break even Point (dollars) = $646,000

3. Unit sales to attain a target profit = 28,000 units and Dollar sales to attain a target profit = $952,000

4. Break even Point (units) = 28,500 units, Break even Point (dollars) = $969,000 and Dollar sales to attain a target profit = $1,428,000.

Explanation:

Variable Cost % = 100% - 30%

                           = 70%

Thus, variable expenses per unit = $34.00 × 70%

                                                       = $23.80

Break even Point is the level of activity where a firm makes neither a profit nor a loss.

Break even Point (units) = Fixed Cost / Contribution per unit

                                        = $193,800 / ($34.00 ×30%)

                                        = $193,800 / $10.20

                                        = 19,000 units

Break even Point (dollars) = Fixed Cost / CM Ratio

                                           = $193,800 / 0.30

                                           = $646,000

Unit sales to attain a target profit = (Fixed Cost + Target Profit) / Contribution per unit

                                                       = ($193,800 + $91,800) / $10.20

                                                       = 28,000

Dollar sales to attain a target profit = (Fixed Cost + Target Profit) / CM Ratio

                                                       = ($193,800 + $91,800) / 0.30

                                                       = $952,000

When variable expenses reduce by $3.40 per unit.

Break even Point (units) = Fixed Cost / Contribution per unit

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Break even Point (dollars) = Fixed Cost / CM Ratio

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                                                       = $1,428,000

6 0
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