Corporate of Norton University

Feb 3rd, 2012
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Ashford University
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formulas in getting or calculating annuity values

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1. Calculating Annuity Values- So, the pre-retirement APR is:EAR = [1 + (APR / 12)]12 - 1= 0.11APR = 12[(1.11)1/12 - 1] = 10.48%-the post-retirement APR is:EAR = 0.08 = [1 + (APR / 12)]12 - 1APR = 12[(1.08)1/12 - 1] = 7.72%- First, we will calculate how much he needs at retirement. The amount needed at retirement is the PV of the monthly spending plus the PV of the inheritance. The PV of these two cash flows is:PVA = $20,000{1 - [1 / (1 + .0772/12)12(20)]} / (.0772/12) = $2,441,554.61PV = $750,000 / [1 + (.0772/12)]240 = $160,911.16- So, at retirement, he needs: $2,441,544.61 + 160,911.16 = $2,602,465.76- He will be saving $2,100 per month for the next 10 years until he purchases the cabin. The value of his savings after 10 years will be:FVA = $2,000[{[ 1 + (.1048/12)]12(10) - 1} / (.1048/12)] = $421,180.66- After he purchases the cabin, the amount he will have left is:$421,180.66 - 325,000 = $96,180.66- He still has 20 years until retirement. When he is ready to retire, this amount will have grown to:FV = $96,180.66[1 + (.1048/12)]12(20) = $775,438.43- So, when he is ready to retire, based on his current savings, he will be short:$2,602,465.76 - 775,4

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