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a father is planning a savings program to put his daughter through college. his daughter is now 13 years old. she plans to enroll the university in five years from now, and it should take her four years to complete her education. currently, cost per year (for everything - food, clothing - tuition , books, transportation and so forth) is $12,500, but a five percent inflation rate in these costs is forecasted. the daughter recently received $7,500 from her fat her as donation for education, and will be deposited into an account paying 8% compounded annually. the rest of the costs will be met by the money father will deposit in the same account, also earning 8%. father will deposit first saving today and until sh e starts to university, 6 equal deposits. his savings should help cover all university costs and will be totally exhausted after the last year. what is the amount of six equal deposits that will be made by the father?

Sagot :

jepessoa

Answer:

$6,106.39

Explanation:

first we must find out the daughter's total university expenses:

college expenses in 5 years = $12,500 x (1 + 5%)⁵ = $15,953.92

we must find the present value of the college costs:

PV = $15,953.92 + [$15,953.92 x 2.7232 (PV annuity factor, 5%, 3 periods)] = $59,399.63

since the daughter already has $7,500, she will deposit that money and will have $7,500 x (1 + 8%)⁵ = $11,019.96 in 5 years, that means that she is $48,379.67

we now have our future value, the interest rate and the number of periods, we are missing the annuity due contributions:

FV = annual contribution x FV annuity due factor

$48,379.67 = annual contribution x 7.9228 (FV annuity due factor, 8%, 6 periods)

annual contribution = $48,379.67 / 7.9228 = $6,106.39

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