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 Financial Mathematics Old FM Forum

#1
05-08-2018, 04:51 PM
 WinePusher SOA Join Date: Aug 2017 Posts: 4
ASM Practice Exam 2 Question 7 Help

Hi all, I am new to this forum so thanks for having me! I have a question about the following question in ASM Practice Exam 2, question 7 for exam FM. The question is:

A perpetuity-immediate pays \$50 per quarter, and has a PV of \$2000 at an annual effective interest rate of i. A 30-year annuity pays \$10,000 at the end of every two years. Using interest rate i, calculate the PV of the 30 year annuity three years prior to the first payment.

The solution gives the effective 2 year rate as .218403 however I don't understand this. My method to arrive at the effective two year rate is as follows:

From the perpetuity, the nominal rate convertible quarterly and the effective quarterly rate are, respectively, .025 and 0.00625.

Thus, the effective annual rate is .025235353.

Finding the effective two year rate using the effective annual rate: (1+i)^(.5)=(1.025235353) => the two year effective rate is .051107529.

Or using the effective quarterly rate, (1+i)^(.5)=(1.00625^4) also gives the two year effective rate as .051107529.

In the solution, Cherry derives the two year effective rate as follows:

(1+i)^(.5)=(1+.025)^4 however in this case .025 is the nominal rate convertible quarterly. Could someone please clarify? Thanks a lot!
#2
05-09-2018, 06:32 PM
 WinePusher SOA Join Date: Aug 2017 Posts: 4

Hey, would anyone be able to assist? Thanks!!
#3
05-14-2018, 04:17 PM
 Chappe Member CAS AAA Join Date: Jan 2005 Location: MO College: MOST Favorite beer: free and cold Posts: 63

From the perpetuity present value equation, 50/(i(4)⁄4)=2000, the nominal interest rate convertible quarterly is 10%. i(4)/4 is 2.5%.
#4
05-14-2018, 07:38 PM
 WinePusher SOA Join Date: Aug 2017 Posts: 4

Thanks a lot Chappe! Stupid mistake on my part.
#5
05-14-2018, 07:40 PM
 WinePusher SOA Join Date: Aug 2017 Posts: 4

Could I also ask, I know FM has 35 questions and the pass rate is 70% correct? Is it true that 5 of the questions are not included in the score?

So to actually pass you would need at least 21 correct questions (.7*30)?
#6
05-17-2018, 06:02 PM
 LilliedActuary SOA Join Date: May 2018 Studying for either MLC or C (unsure) College: University of Northern Iowa Alumni Posts: 2

Quote:
 Originally Posted by WinePusher Could I also ask, I know FM has 35 questions and the pass rate is 70% correct? Is it true that 5 of the questions are not included in the score? So to actually pass you would need at least 21 correct questions (.7*30)?
WinePusher;

It is true that there are some "pilot" questions that will not be scored. It would be wisest to head in trying to get all 35 questions right and not necessarily focus on beating the 70% mark.

However with that being said, yes your math would be correct.