Appropriate formula to find future value

Question

Use the appropriate formula to find the future value (in $) of $700 deposited at the beginning of every six months, for 19 years if a bank pays 4% interest, compounded semiannually. (Round your answers to the nearest cent.)

Answer 1

The $700.00 payments are deposited at the beginning of every six months (with 2×19 or 38 six-month compounding periods in 19 years). It then follows that one seeks the amount of "an annuity due".

An Annuity Due amounts to the Annuity Future Value for one more than the number of Compounding Periods Minus one Payment Amount.

That is, one would calculate [700(1 + 0.04/2)^(2×19+1) − 700] Divided By (0.04/2) Minus 700, which comes

to $40066.06689 or $40066.07.