You want to start saving for your retirement, which you expect 32 years from now
ID: 2726397 • Letter: Y
Question
You want to start saving for your retirement, which you expect 32 years from now. To do this, you will invest $1,200 every month until then. You decide to allocate your savings as follows: $950 per month in a stock fund with an expected APR return of 8% $250 per month in a bond fund with an expected APR return of 2% At your retirement, you will redeem all of your investments and put them into a new consolidated account with a 4% return. But you will also make monthly withdrawals over the 25 years of your expected life following retirement.
a) What will be the total (nominal) dollar value of the two accounts when you transfer the funds to the new consolidated account at the end of 32 years?
b) How much will you be able to withdraw from your account each month during your 25year retirement?
Explanation / Answer
a)
Future value of annuity = Annuity*{(1+r)n-1}/r
Monthly rate of return for stock fund = 8%/12 = 0.67%
Compounding period of retirement = 32 years *12 = 384 months
Value of investment in stock fund after 32 years = $950*(1.0067384 – 1)/0.0067 = $950*1789.63 = $1,700,148.50
Monthly rate of return for bond fund = 2%/12 = 0.17%
Value of investment in bond fund after 32 years = $250*(1.0017384 – 1)/0.0017 = $250 * 541.09 = $135,272.50
Total value of the two accounts at the end of 32 year = $1,700,148.50 + $135,272.50 = $1,835,421
b)
Monthly rate of return for consolidated fund = 4%/12 = 0.33%
No. of monthly withdrawals = 25 years *12 = 300
Monthly withdrawal = (Investment*r)/{1-(1+r)-n}
Monthly withdrawal = ($1,835,421*0.0033)/(1-1.0033-300) = $6,056.89/0.6278 = $9,647.80
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