Actuarial & Insurance

Intermediate

Present Value of an Annuity

Value today of a stream of future payments.

Formula

PV = P \frac{1 - (1+r)^{-n}}{r}

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Variables

PVPresent value

PPayment per period

rInterest rate

nNumber of periods

Example

P=$10k, r=4%, n=20: PV ≈ $135,900

Did You Know?

Pension providers use this to work out the lump sum needed to fund a lifetime of retirement payments.

actuarial annuity pension

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More in Actuarial & Insurance

Pure Premium

Expected claim cost per policy: frequency times severity.

Gross Premium

Premium that covers claims plus an expense/profit load.

Loss Ratio

Claims paid divided by premiums earned.

Combined Ratio

Total cost ratio: losses plus expenses vs premium.

Expected Value of a Claim

Probability-weighted average of possible claim amounts.

Future Value of an Annuity

Accumulated value of regular contributions.