I need some help with this homework problem, would appreciate it.

You estimate that by the time you retire in 35 years, you will have accumulated savings of \$2 million. If the interest rate is 8% and you live 15 years after retirement, and assume there is a 4% inflation rate, work out a spending program for your retirement that will allow you to increase your expenditure in line with inflation.

So from what I see, the yearly expenditure increases by a factor of 1.04, and the leftover savings earn an interest rate of 8%.

I assume that the savings are withdrawn at the start, so at the start of yr 1, .., start of yr 15.

Ok, so my workings are

[C/(r-g)]x[1-((1+g)/(1+r))^n]x(1+r) = PV

where PV = 2,000,000 r=0.08, g=0.04.

I obtain C = 171,361.66 So the first payment at the start of year 1 is C, the 2nd payment is C*1.04, ..., the 15th payment is C*1.04^14.

Is this correct?

• I don't think HW problems are encouraged here, but I'll tell you your answer is correct. My love of equations faded with the advent of good cheap finance calculators and spreadsheets. in this case a spreadsheet confirms the result using just 4 function math and a number of iterations (guesses), 10 or so. Commented Jan 1, 2012 at 15:53
• @JoeTaxpayer At electronics.SE we allow homework questions as long as it is still an acceptable question as far as the sites standards are concerned. So essentially, remove any references to it being a homework question, and if it is still a good question then it can stand. The problem with this question is an answer could simply be "Yes" and nothing else. It is good to see effort on the part of the OP, but it also has to have room for a good answer. Commented Jan 1, 2012 at 21:04

Yes, it is correct.

``````Year Withdrawal Jan 1  Amount Dec 31
0                       \$2,000,000.00
1    \$171,361.66        \$1,974,929.41
2    \$178,216.13        \$1,940,450.34
3    \$185,344.77        \$1,895,514.02
4    \$192,758.56        \$1,838,975.89
5    \$200,468.90        \$1,769,587.55
6    \$208,487.66        \$1,685,987.88
7    \$216,827.17        \$1,586,693.56
8    \$225,500.25        \$1,470,088.78
9    \$234,520.26        \$1,334,413.99
10   \$243,901.07        \$1,177,753.95
11   \$253,657.12        \$998,024.58
12   \$263,803.40        \$792,958.87
13   \$274,355.54        \$560,091.60
14   \$285,329.76        \$296,742.79
15   \$296,742.95        \$(0.18)
``````