Answer to Question #157012 in Financial Math for Wachira Ann Wangari

Question

a) consider a car owner who has an 80% chance of no accidents in a year, a 20% chance of being a single accident in a year. For simplicity, assume that there is a 50% probability that after the accident the car will need repairs costing ksh 500, a 40% probability that the repairs will cost kshs 5,000 and a 10% probability that the car will need to be replaced which will coat kshs 15,000. Combine the frequency and severity distribution to form

I) distribution of the random variable X, loss due to accident

II) what is the car owners expected loss

III) what is the potential variability of the loss incurred.

b) You want to take out a mortgage of kshs 200,000 on your house and you offered an interest rate of 6% on a 15 year mortgage. Interest is compounded monthly. What is your monthly repayment.

Answer 1

a) i) Let $X$ is loss for the year. Then:

ii) $E(X)=0\cdot0.8+500\cdot0.1+5000\cdot0.08+15000\cdot0.02=\$750$

iii) The mean of loss:

$\overline{X}=\frac{0+500+5000+15000}{4}=\$5125$

Standard deviation:

$s=\sqrt{\frac{(0-5125)^2+(500-5125)^2+(5000-5125)^2+(15000-5125)^2}{4}}=\$6024.69$

b)

$R=\frac{Pr}{1-(1+r)^{-n}}$

$P=200000, r=0.06, n=15\cdot12=180$ month

$R=\frac{200000\cdot0.06}{1-1.06^{-180}}=12000.33$