How much can be withdrawn from this fund at the beginning of each half-year for the next 4 years if the fund earns 7.7%, compounded semiannually?

Question

Recent sales of some real estate and record profits make it possible for a manufacturer to set aside $1,000,000 in a fund to be used for modernization and remodeling. How much can be withdrawn from this fund at the beginning of each half-year for the next 4 years if the fund earns 7.7%, compounded semiannually?

Solve the problem. (Round your answer to the nearest cent.) 

Answer 1

Here is another annuity, but in this case we have the present value and want to find the payment. (Have a look at the answer to the other question you posted)

Again define the discount rate v = 1/ (1 + .077/2), let P be the payment (or withdrawal for this particular example).

1000000 = P * ( v⁰ + v¹ + ... + v⁷)

Since withdrawals are at the beginning of the year the first withdrawal is not discounted at all, and the last payment is discounted 7 semi-annual periods.

Solving for P = 142136.97