You are trying to calculate how much money you should have at retirement. On you
ID: 2653323 • Letter: Y
Question
You are trying to calculate how much money you should have at retirement. On your 58th birthday you will retire and immediately make your first withdrawal of $5,000.00. You plan to make 26 such withdrawals each year. You plan to continue withdrawing at that level and frequency until you are 85 years old. (Assume beginning of period withdrawals with the first withdrawal on your retirement date and no withdrawal on your final birthday.) During retirement your savings will earn only 3.9% per annum. How much do you have to have saved at retirement to fund these planned withdrawals?
Explanation / Answer
Answer:
Calculation of amount required at retirement using present value of annuity due formula :
Present value of annuity due = P + P* [{1-(1+r)^-(n-1)} /r]
P = $5000
r = 3.9% = 0.039
n= 26
Present value of annuity due = 5000 + 5000* [{1-(1+0.039)^-(26-1)} /0.039]
= 5000 + [5000 * (1-0.38424773) /0.039]
= 5000 + 78942.60
= $83942.60
Hence amount required at retirement = $83942.60
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