Present Value

Question 1

On March 15, year 1, Ashe Corp. adopted a plan to accumulate $1,000,000 by September 1, year 5. Ashe plans to make four equal annual deposits to a fund that will earn interest at 10% compounded annually. Ashe made the first deposit on September 1, year 1. Future value and future amount factors are as follows:
Future value of $1 at 10% for 4 periods 1.46
Future amount of ordinary annuity of $1 at 10% for four periods 4.64
Future amount of annuity in advance of $1 at 10% for four periods 5.11
Ashe should make four annual deposits (rounded) of
250,000
195,700
146,000
215,500

Answer 1

The desired fund balance on September 1, year 5 ($1,000,000) is a future amount. The series of four equal annual deposits is an annuity in advance, as illustrated in the diagram below.
This is an annuity in advance, rather than an ordinary annuity, because the last deposit (9/1/y4) is made one year prior to the date the future amount is needed. Therefore, these are beginning-of-year payments. The deposit amount is computed by dividing the future amount by the factor for the future amount of an annuity in advance.
$1,000,000 / 5.11 = $195,700