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Assume that your parents wanted to have $150,000 saved for college by your 18th birthday and they started saving on your first birthday. They saved the same amount each year on your birthday and earned 12.0% per year on their investments.
a. How much would they have to save each year to reach their​ goal?

Respuesta :

Edufirst

Answer:

        [tex]\large\boxed{\large\boxed{\$2,690.60}}[/tex]

Explanation:

The situation described corresponds to a constant annuity for a series of years. This is the value of a series of annual contant payments, at a constant rate.

The formula to calculate the future value of constant annuity, starting a year from today, is:

    [tex]FV_{annuity}=\dfrac{(1+r)^n-1}{r}\times annual\text{ }investment[/tex]

Where:

  • r is the constant interest rate: 12.0% = 0.12
  • n is the number of years: 18
  • [tex]FV_{annuity}=\$150,000[/tex] (the goal)
  • Annual investment: is the amount they have to save each year to reach their goal.

Substitute and solve for tha annual investment:

        [tex]\$150,000=\dfrac{(1+0.12)^{18}-1}{0.12}\times annual\text{ }investment\\\\\\annual\text{ }investment=\$150,000/55.749715=\$2,690.60[/tex]

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