Question

Find the periodic withdrawals PMT for the given annuity account. (Assume end-of-period withdrawals and compounding at the same intervals as withdrawals. Round your answer to the nearest cent.)

1. $300,000 at 7%, paid out monthly for 19 years

2. $45,000 at 6%, paid out quarterly for 19 years

Answer 1

Part 1 :

PV of Annuity:

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

PV of Annuity = Cash Flow * [ 1 - [(1+r)^-n]] /r
r - Int rate per period
n - No. of periods

Particulars	Amount
PV Annuity	$      3,00,000.00
Int Rate	0.583%
Periods	228

Cash Flow = PV of Annuity / [ 1 - [(1+r)^-n]] /r
= $ 300000 / [ 1 - [(1+0.0058)^-20]] /0.0058
= $ 300000 / [ 1 - [(1.0058)^-20]] /0.0058
= $ 300000 / [ 1 - 0.2655 ] /0.0058
= $ 300000 / [0.7345 / 0.0058 ]
= $ 300000 / 125.9141
= $ 2382.58
Monthly withdrawl is $ 2382.58

Part 2:

PV of Annuity:

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

PV of Annuity = Cash Flow * [ 1 - [(1+r)^-n]] /r
r - Int rate per period
n - No. of periods

Particulars	Amount
PV Annuity	$          45,000.00
Int Rate	1.500%
Periods	76

Cash Flow = PV of Annuity / [ 1 - [(1+r)^-n]] /r
= $ 45000 / [ 1 - [(1+0.015)^-20]] /0.015
= $ 45000 / [ 1 - [(1.015)^-20]] /0.015
= $ 45000 / [ 1 - 0.3225 ] /0.015
= $ 45000 / [0.6775 / 0.015 ]
= $ 45000 / 45.1641
= $ 996.37
Quarterly withdrawl is $ 996.37