Question

ABC Company wants to have $82,761 in nine years. The company intends to
accumulate that amount by making equal semi-annual cash deposits at the
beginning of every six months for nine years into a bank account that
pays 10% interest compounded semi-annually.

Calculate the amount of each semi-annual deposit.

Use the time value of money factors posted in carmen to answer this question.
To access these factors, click modules and then scroll to week 12. Click on
the link labeled present & future value table factors. No credit will be
awarded for this question using a means other than these table factors to
answer this question.

Answer 1

As the question requires to calculate semiannual payments required to reach the goal, interest rate = 10%/2 = 5%; Number of periodic payments 9 years x 2 = 18. As the payment is required to be made at the beginning of each semiannual, table to be referred is Annuity due factor table of FVA of $1 at 5% for 18 periods. Therefore, Periodic payment required Target future value / Annuity factor: Target future value: $82,761, Annuity factor: 29.5390 [Ref: Annuity due factor table of FVA of $1 at 5% for 18 periods], Periodic payment required: $2,801.75 [$82,761/29.539]