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You anticipate having to pay $30,000 per year for your child’s college education starting 10 years from now. You plan to finance four years of college by making quarterly deposits in a savings account starting now. The final deposit is made three months prior to the first college payment, for a total of 40 deposits. Each annual college payment is made in full at the beginning of the school year. If the savings account earns 8% per annum convertible quarterly, what should your quarterly deposit be?

Respuesta :

jepessoa

Answer:

$1,741.81

Explanation:

we must first determine the total cost of college using the present value of an annuity due:

present value = $30,000 x 3.5771 (PV factor annuity due, 8%, 4 periods) = $107,313

to find the quarterly payment we can use the following formula:

future value of an annuity due = quarterly payment x FV annuity factor (2%, 40 periods)

  • future value of annuity due = $107,313
  • FV annuity factor (2%, 40 periods) = 61.61002

$107,313 = quarterly payment x 61.61002

quarterly payment = $107,313 / 61.61002 = $1,741.81

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