the academy for academic excellence has just announced their winner for the most successful student in mathematics. this student will receive a grant for their college education as well as national recognition for academic excellence in the field of mathematics. the grant will cover $12,177.17 of the cost of school per year for 5 years. if the initial amount is invested into an account over the five years, paying an annual interest rate of 5.5%, and you are to withdraw from this account until the remaining balance after the 5 years is zero dollars, determine the initial amount of the grant. round your answer to the nearest dollar.

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12-10-2022
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the academy for academic excellence has just announced their winner for the most successful student in mathematics. this student will receive a grant for their college education as well as national recognition for academic excellence in the field of mathematics. the grant will cover $12,177.17 of the cost of school per year for 5 years. if the initial amount is invested into an account over the five years, paying an annual interest rate of 5.5%, and you are to withdraw from this account until the remaining balance after the 5 years is zero dollars, determine the initial amount of the grant. round your answer to the nearest dollar.

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contexto1016 contexto1016 · Answer 1 · 2022-10-20T22:30:50+02:00

The correct answer to the question is $52000. The annual withdrawal amount is $12,177.17. To determine the grant's initial amount, the Annuity's PV.

It has to be calculated:

Now, r = 1.055 and a = 12177.17.

Let x(0) equal the starting sum.

The amount increases to rx(0) after a year, then decreases to rx(0) - a. The sum after a year is therefore x(1) = rx(0) - a.

Annual withdrawal (A) = $12,177.17

r = 5.5%

n = 5 years

PV of Annuity= PMT * [1 - [(1 / 1+r)]/r],

Where P stands for present value,

PMT stands for the sum of each payment.

r = Interest or discount rate.

Now, PV of Annuity= 12177.17*[1-(1/1+0.55)]/5.5%]

=$52000 (approx)

To learn more about PV annuity, the given link:

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