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An annuity has a $50,000 principal, a 7% rate and a 3 year payout period. How much is each annual payout?
payout = $50,000 • .07 • (1 + .07)3 ÷ [ (1 + .07)3 -1 ]
payout = 3,500 • 1.225043 ÷ [ 1.225043 -1 ]
payout = 4,287.65 ÷ [ .225043 ]
annual payout = 19,052.58
At the end of the first year, the $50,000 principal has earned $3,500.00 interest (50,000 × .07 = $3,500.00) increasing the annuity balance to $53,500. After the first annual payout of $19,052.58, the balance is reduced to $34,447.42.
At the end of the second year, the $34,447.42 balance has earned $2,411.32 interest ($34,447.42 × .07 = $2,411.32) increasing the annuity balance to $36,858.74. After the second annual payout, the balance is reduced to $17,806.16.
At the end of the third year, the $17,806.16 balance has earned $1,246.43 interest ($17,806.16 × .07 = $1,246.43) increasing the annuity balance to $19,052.59. Now when the third annual payout is made, the balance is reduced to zero. (Okay, the balance is .01 but that's close enough).
Looking at the mathematics involved with a manually calculated payout, it's much easier to use the calculator isn't it?
1728 Software Systems
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