Question

You are planning to save for retirement over the next 30 years. To save for retirement, you will invest $1,900 per month in a stock account in real dollars and $615 per month in a bond account in real dollars. The effective annual return of the stock account is expected to be 12 percent, and the bond account will earn 7 percent. When you retire, you will combine your money into an account with an effective return of 8 percent. The returns are stated in nominal terms. The inflation rate over this period is expected to be 5 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.)

Answer 1

Px[(1+r)An-1r Stock a/c balance after 25 years Here, 6.47%-((1+(1+12%)(1+5%)-1)^(1/12)-1)*12 1 Interest rate per annum 2 Number of years 30 3 Number of payments per per annum 12 1:3 Interest rate per period (r) 2x3 Number of periods (n) Payment per period (P) 0.54% 360 $ 1,900 Stock a/c balance after 25 years $ 2,090,028.84 Px[(1+r)An-1]r Bond a/c balance after 25 years Here, 1.89%((1+(1+7%)/(1+5%)-1)^(1/12)-1)*12 1 Interest rate per annum 2 Number of years 30 3 Number of payments per per annum 12 1:3 Interest rate per period (r 0.16% 2x3 Number of periods (n) 360 Payment per period (P) $ 615 Bond a/c balance after 25 years 297,533.63 Total value in retirement account after 25 years i.e. after retirement (Stock+Bond) $ 2,387,562.47

PVA:([1-(1(1+r)An)] r) Real monthly withdrawal Here, 2.82%(1+(1+8%)(1+5%)-1)^(1/12)-1)*12 A Interest rate per annum B Number of years 25 CNumber of compoundings per per annum A C Interest rate per period (r) BxC Number of periods (n) Present value (PVA) 12 0.24% 300 2,387,562.47 Real monthly withdrawal $11,100.32 Last nominal withdrawal $ 162,460.18 -C40*(1+5%)A55

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