Answer:
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.
