# Tagged Questions

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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### Actuarial Problem. (Policyholder).What is the probability that a new policyholder will have an accident within a year of purchasinag a policy?

Problem said: Suppose people can be divided into two classes: those who are accident-prone and those who are not. The statistics show that an accident-prone person will have an accident at some ...
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### What is the pdf of $Z=X/\max(X,Y)$ with $X,Y$ exponentials of lambda parameter?

Given $X,Y$ 2 independent r.v.'s both distributed as $\exp(λ)$, what is the pdf of $Z=X/\max(X,Y)$?
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### Annuity-Immediate Problem with Varying Payment (ASM FM Study Manual 10th Edition, Practice Exam 2 P.679 Q1)

The question asks: 'A 35-year annuity immediate pays $1.05^{35}$ in the first year, $1.05^{34}$ in the second year, etc., until 1.05 is paid in the 35th year. The PV of this annuity at 5% effective is ...
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### Effective Rate of Discount and Continuous Interest

I have two problems that I am having trouble with Using an interest rate of 5%, find the present value of 5000 payable in 10 years and the effective rate of discount between the 7th and 8th year. ...
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### Calculating the standard deviation involving a moment generating function

An actuary determines that the claim size for a certain class of accidents is a random variable, X, with moment generation function: $$M_X(t)=\frac{1}{(1-2500t)^4}.$$ Calculate the standard deviation ...
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### 128 factories close down first

I found this problem on http://poissonlabs.com/blog/how-insurance-works. I'm not quite sure how to solve it. Suppose that $1000$ factories belong to an industry, and that each factory faces an ...
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### Finding ratio of interest rates

I'm reading through Marcel B. Finan's A Basic Course in the Theory of Interest and Derivatives Markets: A Preparation for the Actuarial Exam FM/2 on my own and am unsure how to proceed with a question ...
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### Exact match of assets and liabilities.

Liabilities of $1$ each are due at then ends of periods $1$ and $2$. There are three securities available to produce asset income to cover these liabilities, as follows: (i) A bond due at the end of ...
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### Functional invariance of exponential stochastic order

I am studying for an exam on stochastic order. I am struggling with a question on functional invariance of exponential order ($\leq_{\mathrm{e}}$), where for r.v.s $X$ and $Y$, X \leq_{\mathrm{e}} Y ...
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### Find the highest price which an investor can pay and still be certain of a yield of:

I'm having trouble understanding this example in Kellison's Theory of interest: Consider a 100 par value 4% bond with semiannual coupons callable at 109 on any coupon date starting 5 years after the ...
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### Calculating the interest rate for an annuity (Exam FM)

I have been searching for a way to solve for the interest rate given the monthly payments of a loan. I would like to set up a problem as the following. $X$=monthly payment , $i$=effective ...
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### Finding drop payment with varying interest rates..

Person A is accumulating a 10,000 fund by depositing 100 at the end of each month starting September 1,2002. If the nominal interest rate on the fund is 12% convertible monthly until May 1,2005, and ...
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### Probability of remaining lifetime using force of mortality

I've been stuck on this question for the past half hour and still have no idea how to solve it... I don't think it's supposed to be very difficult but I'm struggling: There are two independent live ...
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### How to derive the variance premium formula

How to derive formula (5.5) with Taylor's expansion in the following link? The difficult part of my question is that i had never seen Var(S) appear in Taylor's expansion http://i.stack.imgur.com/...
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### Financial Mathematics Question: Payable

I am trying to solve the following problem and I am not quite sure what it means. A loan of 100,000 is payable over five years with monthly payments of 60,000 commencing one month after the ...
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### Determination of Bond prices

Two 1000 dollar face value bonds are both redeemable at par, with the first having a redemption date 3 years prior to the redemption date of the second. Both are bought to yield 11 percent convertible ...
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### Effective Rate of Interest and Inflation Problem

I'm trying to solve the following question from a past SOA FM exam, but there are no posted solutions so I'm not sure if I'm headed in the right direction. John deposits 10, 000 in a saving ...
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### Theory of Interest - Going from discount rate - annual effective and nominal to force of interest

[![Force of Interest & Discount Rate][1]][1] Hi there guys, I'm new to Theory of Interest and I might have started studying a bit too late, but I really need to just grasp this before the end of ...