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 Financial Mathematics Old FM Forum

#1
09-14-2019, 09:21 PM
 Berkmaster SOA Join Date: Jun 2019 College: CSUN Posts: 25
FM Question

"John borrows 10,000 from Tony and agrees to repay the loan with 10 equal annual installments of principal plus interest on the unpaid balance at 5% effective. Immediately after the loan is made, Tony sells the loan to Chris for a price which is equal to the present value of John's future payments calculated at 4%. Calculate the price that Chris will pay for the loan."

The answer in the back of the book (Finan, 41.2) is 10,472.28 but I get 10,503.98.

It seems straightforward. 10,000 * a_10_.04 / a_10_.05. I would appreciate your feedback. Thank you.
#2
09-14-2019, 09:41 PM
 Breadmaker Member SOA Join Date: May 2009 Studying for CPD - and nuttin' else! College: Swigmore U Favorite beer: Guinness Posts: 5,576

If I treat it as an immediate annuity, I get 10,503.98; if I treat it like an annuity due, I get 10,403.98.

Is there errata for this question?
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#3
09-14-2019, 09:46 PM
 Academic Actuary Member Join Date: Sep 2009 Posts: 9,149

The loan isn't paid in equal installments, it's paid in equal installments of principal.
#4
09-14-2019, 09:47 PM
 Gandalf Site Supporter Site Supporter SOA Join Date: Nov 2001 Location: Middle Earth Posts: 31,366

Neither, you are both interpreting the payment stream differently from the Finan's intent.

He means (10 equal annual installments of principal, thus 1000 each) (plus interest on the unpaid balance at 5% effective)

If he meant a level annuity, wouldn't you expect him to just say 10 equal annual installments? or 10 equal annual installments of principal and interest?

The wording certainly could have been clearer and I hope and think it would be on an exam question.

ninja'd
#5
09-14-2019, 09:47 PM
 Breadmaker Member SOA Join Date: May 2009 Studying for CPD - and nuttin' else! College: Swigmore U Favorite beer: Guinness Posts: 5,576

Quote:
 Originally Posted by Academic Actuary The loan isn't paid in equal installments, it's paid in equal installments of principal.
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#6
09-15-2019, 01:25 AM
 Berkmaster SOA Join Date: Jun 2019 College: CSUN Posts: 25

Thank you very much. While I find Finan's book to be a great book in terms of education, he does leave much to be desired quite often on his wording.

I've found many many typos.