1) Recently, Glenda Estes was interested in purchasing a Honda Acura. The salesp

ID: 2774827 • Letter: 1

Question

1) Recently, Glenda Estes was interested in purchasing a Honda Acura. The salesperson indicated that the price of the car was either $27,600 cash, or $6,900 at the end of each of 5 years. Compute the effective interest rate to the nearest percent that Glenda would pay if she chooses to make the five annual payments.

2) Recently, property/casualty insurance companies have been criticized because they reserve for the total loss as much as 5 years before it may happen. The IRS has joined the debate because it says the full reserve is unfair from a taxation viewpoint. What do you believe is the IRS position?

Explanation / Answer

Formula for loan amortization =

A= [i*P*(1+i)^n]/[(1+i)^n-1]

Amt $

A = periodical installment

=6900

P=Loan amount =

=27600

i= interest rate per period =

required

n=total no of payments

Therefore

6900 = [i*27600*(1+i)^5]/[(1+i)^5-1]

Or , [i(1+i)^5]/[(1+i)^5-1]=0.25

Or i=8% approx

The recent IRS view on unpaid Loss reserve by property /casualty insurance companies is to test the unpaid loss reserve by "Age-toUltimate Method," or the "Paid Loss Extrapolation Method”.

The method assumes that, because losses develop according to a pattern that remains relatively constant from year-to-year, the actual development of paid losses at any time can be extrapolated to the ultimate total of losses to be paid.

The method depends on creating a matrix of developed losses at successive stages, referred to as the "loss development pattern." This pattern will show that X% of losses are paid after one year, Y% of losses are paid after two years, etc.

It is possible to estimate the amount of losses that ultimately will be paid by using this method.

The amount of the reserve being held should equal the ultimate amount of losses minus the amount of losses already developed. If the reserve exceeds that amount, the IRS may claim that the reserve is redundant.