Question

find the present value of the decreasing annuity necessary to fund a withdrawal of 1700/quarter for 20 years, if the annuity earns 3%/year. (assume end of period deposits and compounding at the same intervals as deposits)

Answer 1

PV of Decreasing Annuity:

Decreasing Annuity is series of cash flows that are withdrawn at regular intervals for specific period of time.

PV of Annuity = Cash Flow * [ 1 - [(1+r)^-n]] /r
r - Int rate per period = 3 % / 4 = 0.75 % or 0.0075
n - No. of periods = 20 years * 4 = 80 quarters

Particulars	Amount
Cash Flow	$            1,700.00
Int Rate	0.7500%
Periods	80

PV of Annuity = Cash Flow * [ 1 - [(1+r)^-n]] /r
= $ 1700 * [ 1 - [(1+0.0075)^-80]] /0.0075
= $ 1700 * [ 1 - [(1.0075)^-80]] /0.0075
= $ 1700 * [ 1 - [0.55004]] /0.0075
= $ 1700 * [0.44996]] /0.0075
= $ 101990.55

PV of Decreasing Annuity = $ 101990.55

Please comment if any further assistance is required.