How much must be invested now to receive $10,000 for 15 years if the first $10,000 is received today and the rate is 9%? Present Value ofPeriods Ordinary Annuity at 9% 14 7.78615 15 8.06069 16 8.31256

$87,862

$87,862. Similar to the computation of the future value of an annuity due factor from the future value of an ordinary annuity table, this question is asking us to compute the present value of an annuity due. We must now convert the present value of an ordinary annuity factor to a present value of an annuity due. They want 15 periods at 9% for the factor, so we must go to the factor for 14 periods (7.78615) and add 1.000 (the present value or future value of one when no time has expired), which gives us 8.78615. We want the present value of a series of payments, where the first payment is received today (at the beginning of the period = annuity due). The present value of an annuity due factor (8.78615) times the value of the annualized payments ($10,000) equals the present value (How much must be invested now?) of $87,862.