What is the amount of 20 equal annual deposits that can provide 40 annual withdrawals when...

What is the amount of 20 equal annual deposits that can provide 40 annual withdrawals when a first withdrawal of $2,000 is made at the end of year 21 and subsequent withdrawals increase at the rate of 3 % per year over the previous year’s withdrawal. Determine the deposit amounts based on the interest rate of 7 % compounded annually.

Solutions

Expert Solution

Withdrawal per annum = $2,000

Rate of increase in withdrawal = 3%

Interest rate = 7%

Present Value of the withdrawals as at Year 21:

Year	Withdrawal	PVF (7%)	PV of Withdrawal
21	$2,000	0.934579439	$1,869.16
22	$2,060	0.873438728	$1,799.28
23	$2,122	0.816297877	$1,732.02
24	$2,185	0.762895212	$1,667.27
25	$2,251	0.712986179	$1,604.94
26	$2,319	0.666342224	$1,544.95
27	$2,388	0.622749742	$1,487.19
28	$2,460	0.582009105	$1,431.60
29	$2,534	0.543933743	$1,378.08
30	$2,610	0.508349292	$1,326.56
31	$2,688	0.475092796	$1,276.97
32	$2,768	0.444011959	$1,229.23
33	$2,852	0.414964448	$1,183.28
34	$2,937	0.387817241	$1,139.05
35	$3,025	0.36244602	$1,096.46
36	$3,116	0.338734598	$1,055.47
37	$3,209	0.31657439	$1,016.02
38	$3,306	0.295863916	$978.04
39	$3,405	0.276508333	$941.47
40	$3,507	0.258419003	$906.28
41	$3,612	0.241513087	$872.40
42	$3,721	0.225713165	$839.79
43	$3,832	0.210946883	$808.39
44	$3,947	0.19714662	$778.17
45	$4,066	0.184249178	$749.08
46	$4,188	0.172195493	$721.08
47	$4,313	0.160930367	$694.12
48	$4,443	0.150402212	$668.17
49	$4,576	0.140562815	$643.20
50	$4,713	0.131367117	$619.15
51	$4,855	0.122773007	$596.00
52	$5,000	0.114741128	$573.72
53	$5,150	0.107234699	$552.28
54	$5,305	0.100219345	$531.63
55	$5,464	0.093662939	$511.76
56	$5,628	0.087535457	$492.63
57	$5,797	0.081808838	$474.21
58	$5,970	0.076456858	$456.48
59	$6,150	0.071455008	$439.42
60	$6,334	0.066780381	$422.99
			$39,107.99

Future value of Deposits = Present Value of withdrawals

Annual Deposit * FVAD(7%, 20) = $39,107.99

Annual Deposit * 43.86517678 = $39,107.99

Annual Deposit = $39,107.99 / 43.86517678

Annual Deposit = $891.5498

ekkarill92 answered 2 years ago

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