Life annuity is a payment (pension), which is paid up to a certain event - usually up to the death of the receiver of the pension -. It is possible to include survivor's pensions.

The life annuities knows by current payments of dues (postponed life annuities) or by payment of an a mark contribution (life annuities immediately beginning) to be acquired. If life annuity is compensated by a single payment, then as amount of number the statistical bar value of the pension is usually disbursed as indemnity.

Application

An application for the life annuities is the purchase of a house. The purchase price becomes on agreement life annuity not completely, but only partial pays (or not at all). The buyer makes a commitment then to the salesman, a part of the purchase price immediately to pay and the remainder as monthly life annuities up to the death of the salesman.

For the salesman it is favourable that he can secure a part of its income for the remainder of his life. For the buyer hope exists the fact that the salesman dies unexpectedly early and so the life annuities ends prematurely. One speaks in such a case of a statistical profit. If no adjustment is intended to the inflation rate, the buyer can in addition for it to hope that its income rises, but the value of the life annuities by the inflation sinks.

Computation

In order to compute the value life annuities, one can the situation mathematically equivalent in such a way represent:

The debtor (buyer of the house) possesses a fortune, which supplies the amount, which is to be transferred to the creditor (receiver of the life annuities, salesmen) by interest charges in each period (monthly, annually) exactly.

Pension = capital \ cdot (q-1)

Principal one is thereby the part of the purchase price, which not immediately, but when life annuity is to be paid. The formula proceeds with constant interest rate at the capital market and from the case, which is most unfavorable for the buyer and eternal life of the creditor (receiver of the life annuities, salesmen) goes out. This is so seen the most favorable value for the salesman, without the salesman is overreached, is thus the computational lower bound for the amount of the life annuities.

If the average life expectancy of the salesman is well-known due to statistic data, then also this formula can be consulted (applies with payment at the end of the payment period, thus

Pension = capital \ cdot (\ frac {q-1} {1 - \ frac {1} {q^n}})

N is the number of interest periods (usually months), which the salesman will statistically still live. The formula results in the most favorable value for the salesman, without the buyer is overreached, is thus the computational upper limit for the amount of the life annuities.

q = \ frac {p \ %} {100 \ %} +1

p is the interest rate for the capital return and must the period by q be adapted. If one proceeds however (as usual with many business) from a monthly payment and interest rate p, which shows the one annual interest charges, then square meter is to use instead of q correct-proves:

q_m = (\ frac {p \ %} {100 \ %} +1) ^ {\ frac {1} {12}}

Over the interest rate p, which cannot be predicted for the future, but to be accepted, can the height of the life annuities must be likewise affected.

See also

Perhaps an unexpectedly high lifetime can lead the calculation ad absurdum, as in case of of Jeanne Calment. An alternative to life annuities is therefore the capital payment.

Articles in category "Life annuity"

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