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
Now that we have the annual payout amount, let’s see how the payout process works.
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?
Upon retirement, you’d like to have an annuity that will pay out $25,000.00 per year for 20 years.
If the annuity interest rate is 8 per cent, how much principal would you need?
Principal = (25,000 • [(1.08)20 -1)] ÷ (.08 • (1.08)20
Principal = (25,000 • 3.6609571438) ÷ (.08 • 4.6609571438)
Principal = 91,523.93 ÷ 0.3728765715
Principal = 245,453.69
You are retiring with a 7% $300,000.00 annuity that pays 50,000.00 per year.
How long will this annuity last?
Years = log (1 ÷ (1 – [300,000 • .07 ÷ 50,000])) ÷ log (1.07)Years = log (1 ÷ (1 – .42)) ÷ 0.0293837777
Years = log (1 ÷ .58) ÷ 0.0293837777
Years = log (1.724137931) ÷ 0.0293837777
Years = 0.2365720064 ÷ 0.0293837777
Years = 8.051109322