You are planning to save for retirement over the next 30 years. To save for reti
ID: 2614831 • Letter: Y
Question
You are planning to save for retirement over the next 30 years. To save for retirement, you will invest $1,750 per month in a stock account in real dollars and $600 per month in a bond account in real dollars. The effective annual return of the stock account is expected to be 13 percent, and the bond account will earn 5 percent. When you retire, you will combine your money into an account with an effective return of 7 percent. The returns are stated in nominal terms. The inflation rate over this period is expected to be 3 percent.
How much can you withdraw each month from your account in real terms assuming a 25-year withdrawal period? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
What is the nominal dollar amount of your last withdrawal? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
You are planning to save for retirement over the next 30 years. To save for retirement, you will invest $1,750 per month in a stock account in real dollars and $600 per month in a bond account in real dollars. The effective annual return of the stock account is expected to be 13 percent, and the bond account will earn 5 percent. When you retire, you will combine your money into an account with an effective return of 7 percent. The returns are stated in nominal terms. The inflation rate over this period is expected to be 3 percent.
Explanation / Answer
Monthly Investments in Stock = $ 1750, Monthly Investments in Bonds = $ 600
These investments are stated in real terms or constant dollar terms or inflation-adjusted terms.
Effective Annual Return of Stock = 13 %, Effective Annual Return of Bonds = 5 %
Both returns are quoted in nominal terms or current value terms of non-inflation adjusted terms.
Hence, the returns need to be converted to real terms as cash flows are in real terms.
Real Effective Annual Return of Stocks = 1.13 / 1.03 = 0.971 or 9.71 % and Real Effective Annual Return of Bonds = 1.05 / 1.03 = 0.0194 or 1.94 %
Further, as investments are made every month it is assumed that compounding is also done on a monthly basis.
Hence, Effective Monthly Return on Stocks = (1.0971)^(1/12) - 1 = 0.00775 or 0.775 %
Effective Monthly Return on Bonds = (1.0194)^(1/12) - 1 =0.0016025 or 0.16025 %
Investment Tenure = 30 years or 360 months
Value of Stock Acoount after 30 years = 1750 x (1.00775)^(360) + 1750 x (1.00775)^(359) + ............+ 1750 = $ 3411222.88
Value of Bond Account after 30 years = 600 x (1.0016025)^(360) + 600 x (1.0016025)^(359) + .........+ 600 = $ 291926.99
Total Account Value = 3411222.88 + 291926.99 = $ 3703149.87
Effectve Nominal Return on the Total Account Value = 7 % per annum
Effective Real Return on the Total Account Value = 1.07 / 1.03 = 0.03883 or 3.883 %
Effective Real Monthly Return on Total Account Value = (1.03883)^(1/12) - 1 = 0.00318 or 0.318 %
Withdrawal Tenure = 25 years or 300 months
Let the monthly withdrawals in real term or constant dollar terms be $ K
3703149.87 = K x (1/0.00318) x [1-{1/(1.00318)^(300)}]
K = $ 19172.33
As prevailing inflation rate is 3 % per annum, the nominal value of the last withdrawal coming in at the end of 25 years after retirement date = 19172.33 x (1.03)^(25) = $ 40142.60
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