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OlgaM077 [116]
2 years ago
12

Ashley and Dwayne are saving for retirement. Their goal is to have $250,000 in 15 years. They open up an account with APR of 3.7

% compounded monthly. How much should they deposit each month to meet their goal?
Mathematics
1 answer:
garri49 [273]2 years ago
6 0
<span>The formula for the future value of an investment with regular contributions is

FV = M((1+r/n)^(nt)-1)(n/r)

   where

   FV = Future value

   M = Deposit per period

   r = Interest rate

   n = number of periods per year

   t = number of years

   So let's solve for M, then substitute the known values and calculate:

   FV = M((1+r/n)^(nt)-1)(n/r) FV/(((1+r/n)^(nt)-1)(n/r)) = M

        250000/(((1+0.037/12)^(12 * 15)-1)(12/0.036)) = M

    250000/(((1+0.003083333)^(180)-1)(324.3243243)) = M

    250000/(((1.003083333)^(180)-1)(324.3243243)) = M

    250000/((1.740454228-1)(324.3243243)) = M

   250000/240.1473172 = M

   1041.027661 = M

       So the monthly deposit should be 1041.03 every month.

   Note: This calculation assumes that the 1st deposit will happen AFTER the 1st month.</span>
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larisa86 [58]

Answer:


Step-by-step explanation:

the best business for this area is The Shoe Hut. This is the case for several reasons. First, there is less competition for custom sporting goods, as the supply in the area is lower. Survey data shows that there are more individuals who desire custom outdoor sporting goods than there are people who desire more coffee shops. Finally, the overall capital required to start and maintain The Shoe Hut is lower. Less equipment is needed, any building can be rented, and if an employee cannot be hired immediately, I can run the store on my own.

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2 years ago
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Burka [1]

Answer:

Step-by-step explanation:

  • pick like terms

x² +  b²/4a² = -c / a + b²/4a²

  • b²/4a² = (b/2a)²

x² + (b/2a)² = -c/a + (b/2a)²

(x + b/2a)² = -c/a + (b/2a)² =  -c / a + b²/4a² = (-4ac+ b²)/4a²

(x + b/2a)² =  (-4ac+ b²)/4a²

  • square root both sides

√{(x + b/2a)²} = √{(-4ac+ b²)/4a²}

x + b/2a = √(-4ac+ b²) / √(4a²) = √(-4ac+ b²) / 2a = √( b²-4ac) / 2a

x + b/2a  =  √( b²-4ac) / 2a

  • subtract b/2a from both sides

x + b/2a -b/2a  =  {√( b²-4ac) / 2a } -b/2a

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2 years ago
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Zolol [24]

Answer:

The Probability found is:

P =  \frac{13}{18}

Step-by-step explanation:

Let x be the 10 cents coin.

Let y be the 25 cents coin.

We have to find all the possible outcomes

1) First coin = 10 cents, Second coin = 10 cents , so

(x,x) = 20

2) First coin = 10 cents, Second coin = 25 cents , so

(x,y) = 35

3) First coin = 25 cents, Second coin = 10 cents , so

(y,x) = 35

4) First coin = 25 cents, Second coin = 25 cents , so

(y,y) = 50

Find the probability of each outcome:

P(x,x) =  \frac{5}{9}\cdot\frac{4}{8}=\frac{20}{72}

P(x,y) =  \frac{5}{9}\cdot\frac{4}{8}=\frac{20}{72}

P(y,x) =  \frac{5}{9}\cdot\frac{4}{8}=\frac{20}{72}

P(y,y) = \frac{4}{9}\cdot\frac{3}{8}=\frac{12}{72}

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Answer:

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