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Sometime when you are getting a quote for a term life insurance, they offer you 3 options:

For a period T, and amount insured A.

  • Fixed (payout is always A in the entire period T)
  • Linear desceding (straight line from A to zero in the period P)
  • Decreasing annuity (it's a curve that decreases faster in the last years of period P)

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When you choose the decreasing annuity one, they ask you to provide an interest rate to adjust the curve. The higher that rate is, the slower the payout decreases over the years.

Does anyone know the formula that controls that behaviour?

Payout(t) = Formula(A,T,t,i)

Being:

t: a specific year
T: total number of years
A: total Amount
i: interest/discount rate

If possible, please provide an example with a chart.

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