Answer:
128 payments
Explanation:
Since the payments begin at the end of the month, the formula for calculating the Future Value (FV) of an Ordinary Annuity is used as follows:
FV = M × {[(1 + r)^n - 1] ÷ r} ................................. (1)
Where,
FV = Future value of the amount = $50,000
M = Annuity payment = $250
r = Monthly interest rate = 8% ÷ 12 = 0.67%, 0.0067
n = number of periods the investment will be made = n
Substituting the values into equation (1), we have:
50,000 = 250 × {[(1 + 0.0067)^n - 1] ÷ 0.0067}
50,000/250 = [(1.0067)^n - 1] ÷ 0.0067
200 * 0.0067 = (1.0067)^n - 1
1.33 + 1 = (1.0067)^n
2.33 = (1.0067)^n
By loglinearizing the above, we have:
ln2.33 = n * ln1.0067
0.8473 = n * 0.0066
n = 0.8473/0.0066
n = 127.52, or 128 months approximately
Therefore, the number of payments to make is approximately 128 payments.
