A personal account earmarked as a retirement supplement contains $292,100. Suppose $250,000 is used to establish an annuity that earns 5%, compounded quarterly, and pays $5000 at the end of each quarter. How long will it be until the account balance is $0? (Round your answer UP to the nearest quarter.)

It will take approximately 78 quarters until the account balance is $0.

Explanation:

This can be calculated using the following formula:

n = log(p / (p - A(q - 1))) / log(q) (1)

Where;

n= Number of quarters it will take until the account balance is $0 = ?

A = Amount used to establish the annuity = $250,000

p = quarterly payment = $5,000

q = 1 + (Annual interest rate / Number of quarters in a year) = 1 + (5% / 4) = 1.0125

Substituting the values into equation (1), we have:

n = log(5000 / (5000 - (250000*(1.0125 - 1 / log(1.0125)

n = log(5000 / (5000 - (250000 * 0.0125))) / log(1.0125)

n = log(5000 / (5000 - 3125)) / log(1.0125)

n = log(5000 / 1875) / log(1.0125)

n = log(2.66666666666667) / log(1.0125)

n = 0.425968732272282 / 0.00539503188670614

n = 78.955739505805

Rounding to the nearest quarters, we have:

n = 78. This because the quartely payment is less than $5000 at the end of the 79th quarter.

Therefore, it will take approximately 78 quarters until the account balance is $0.

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