# Questions tagged [actuarial-science]

Actuarial science is a discipline that uses mathematics and statistics to assess risk. The mathematics involved in actuarial science includes probability, statistics, finance, life insurance mathematics, and more.

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### Present value of perpetuity with one extra payment

Consider the perpetuity that pays $3$ by the end of the 2nd year and then every $4$ years. I need to calculate the present value of it when $i=0.05$. So the second payment will be at 6th year. I ...
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### Varying payment- with both increasing and decreasing annuity

I am trying to find the present value of an annuity-immediate such that the first payment is $1000$, and each subsequent payment increases by $100$ until the payments reach $2000$, but then decreases ...
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### Present values of two perpetuities

I have two perpetuities: Pays $1$ at the beginning of every year Pays $1.8$ at the beginning of every odd year I have to show which one is more profitable if $i=0.05$. I calculated present value of ...
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### Interpreting the deferred probabilities of a life aged x will survive for n years but die during the subsequent m years

I am a little bit confused when trying to interpret $_{n|m}q_x$, which I understand is the probability that a life aged x will survive for n years but die during the subsequent m years. However when I ...
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### annuity- find the present value of varying payments

I am trying to find the present value of an annuity, where we have a $20$-year annuity immediate where the first payment is $1000$, and each subsequent payment is increased by either $50$ for the ...
In force of mortality, one divides the probability of failure in a time interval $(x, x+\Delta x)$ by $\Delta x$. Apparently, this gives an annualised instantaneous rate of failure. In this article, a ...