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.

since the options are not listed, when you are working on your budget you should also add water, tv, internet, miscellaneous and your 'fun' money for in your budget. when budgeting, you need to allow for fun money, and mis/accidental money so that you stick to the budget and not go crazy because you feel strapped to the budget.

two years ago, when picking flowers in the mountains back of yosemite valley, i found a book. it was blotted and storm-beaten; all of its outer pages were mealy and crumbly. the paper seemed to dissolve like the snow beneath which it had been buried, however; many of the inner pages were well preserved. and although all were more or less stained and torn, whole chapters were easily readable. this is the condition of the great open book of yosemite glaciers today; its granite pages have been torn and blurred by the same storms that wasted the castaway book.

two years ago, when picking flowers in the mountains back of yosemite valley; i found a book. it was blotted and storm-beaten, all of its outer pages were mealy and crumbly. the paper seemed to dissolve like the snow beneath which it had been buried, however, many of the inner pages were well preserved. and although all were more or less stained and torn; whole chapters were easily readable. this is the condition of the great open book of yosemite glaciers today, its granite pages have been torn and blurred by the same storms that wasted the castaway book.