you are planning your retirement in 10 years. you currently have $150,000 in a b
ID: 2662403 • Letter: Y
Question
you are planning your retirement in 10 years. you currently have $150,000 in a bond account and 450,000 in a stock account. you plan to add $9,000 per year at the end of the next 10 years to your bond account. the stock account will earn an 11.5% return and the bond account will earn a 7.5% return. when you retire you plan to withdraw an equal amount for each of the next 25 yeara at the end of each year and have nothing left. Additionally, when you retire you will transfer your money to an account that earns 6.75%. how much can you withdraw each year?Explanation / Answer
This question has multiple parts. Lets list them out beforesolving for easy understanding. A. Bonds 1. PV = 150,000. This will earn 7.5% pa Coupon rate pa fornext 10Yrs. So here we will calculate FV = PV (1+i)^N =150,000*(1+7.5%)^10 = 309154.73 2. Annual addl Bond investment of 9000 is an Ordinary annuityfor 10 yrs which will pay 7.5% pa. Here FVA = PMT(FVIFAi,n). PMT= 9000. & FVIFAi,n = [(1+i)^n-1]/i. So FVA =9000*[(1+7.5%)^10 - 1]/7.5% = 9000*14.15 =127,323.79 B. Stock A/C PV = 450,000. Int earned = 11.5%. So Stock value at end ofN=10Years = FV = PV(1+I)^N ie FV = 450000*(1+11.5%)^10 = 450000*2.97 = 1,336,476.07 So total amount available at end of 10 yrs = 309,154.73 +127,323.79 + 1,336,476,07 = 1,772,954.59 Now we need to find the PMT which we can withdraw every yearfor Next n=25yrs while the Int i = 6.75%. ie Present value of annuity PVA = PMT(PVIFAi,n). So PMT = PVA/(PVIFAi,n) = PVA/(1/i - 1/(i(1+i)^n)) =1772954.59/(1/6.75% - 1/(6.75%*(1+6.75%)^25)) = 1,772,954.59/11.92= 148,727.69 Thus you can withdraw at end of everyyear $148,727.69 for 25 years to exhaust yourcorpus.Related Questions
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