Calculating the Number of Payments. You’re prepared to make monthly payments of $250, beginning at the end of this month, into an account that pays 8 percent interest compounded monthly. How many payments will you have made when your account balance reaches $50,000?

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.

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