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#1
01-21-2013, 05:08 PM
 msh210 Non-Actuary Join Date: Jan 2013 Posts: 3
finding interest rate (annuity)

I see many old FM exam problems that require the solver to find the interest rate of an annuity (or amortized loan or coupon bond). You wind up with a polynomial in i (or 1/(1+i)) that is pretty much impossible to solve without interpolating along a annuity table (or using Newton's method). How is one supposed to solve these?
#2
01-21-2013, 05:18 PM
 algebrat Member Non-Actuary Join Date: Nov 2012 Location: Ork Studying for GED Favorite beer: Scieoclean Posts: 2,143

Quote:
 Originally Posted by msh210 I see many old FM exam problems that require the solver to find the interest rate of an annuity (or amortized loan or coupon bond). You wind up with a polynomial in i (or 1/(1+i)) that is pretty much impossible to solve without interpolating along a annuity table (or using Newton's method). How is one supposed to solve these?
consider that on the exam it will be multiple choice. thus you don't really need to solve the polynomial, simply evaluate at multiple values.

also, i use the multiview calculator, which allows for table input to a function, thus allowing to test values at a quick rate.

the ba 2 plus calculator (i have professional), will solve for interest rates in basic annuities, and cash flows with no more than 48 types.

one lesser known reason to get the professional (as opposed to basic model ba2plus), is it defaults to P/Y=1, as opposed to 12. amirite?

note that bonds often have small changes in principal C-P (as opposed to loans), so this may be why they include an approximate formula for the interest rate. (And why they give a straight line approximation to the bond table.)

Last edited by algebrat; 01-21-2013 at 05:31 PM..
#3
01-21-2013, 06:42 PM
 Gandalf Site Supporter Site Supporter SOA Join Date: Nov 2001 Location: Middle Earth Posts: 31,363

Quote:
 Originally Posted by algebrat the ba 2 plus calculator (i have professional), will solve for interest rates in basic annuities, and cash flows with no more than 48 types. one lesser known reason to get the professional (as opposed to basic model ba2plus), is it defaults to P/Y=1, as opposed to 12. amirite?
Yes, financial calculators are allowed and can do any of the calculations directly with relatively few key strokes. I don't know the specifics of ba2plus vs professional.
#4
01-21-2013, 06:48 PM
 msh210 Non-Actuary Join Date: Jan 2013 Posts: 3

Ah, thank you, algebrat, Gandalf.
#5
01-22-2013, 11:30 AM
 Phileas Fogg Member SOA Join Date: Dec 2012 Posts: 1,458

I have one additional suggestion if you're doing the "hunt-and-peck" rather than using a financial calculator.

Don't plug in all 5 values. You can usually get by just plugging in 2 of them.

For example, assume that your choices are

(A) 3%
(B) 4%
(C) 5%
(D) 6%
(E) 7%

(Usually they are in ascending or descending order; if they aren't, rearrange them).

Plug in the values for (B) and (D). One of 3 things is likely to happen:

(1) Your answer for (B) or for (D) is really close, and you're going to pick one of them.

(2) You can tell that your answer for (B) is way too high and for (D) is way too low (or vice versa). In this case, you'll want to pick (C)

(3) Both (B) and (D) are wrong, and both are too high (or too low). In that case, one of them will be notably closer, and you'll know which to select between (A) and (E).

The reason this (USUALLY) works is that MOST of the financial functions you'll be working with are monotone increasing or decreasing functions and relatively linear. So once you've plugged in values for (B) and (D), you could approximate the rest pretty accurately with a straight line.

There are two reasons I don't recommend starting with (C) in the middle and using your intuition to decide whether to go up or down:

(1) Calculating (B) and (D) solves it in two choices, which you really aren't going to better than just starting with (C) - you then will typically try (A) [Or (E)] and then decide between that, (C), or the one in the middle.

(2) Occasionally your intuition might slip up and you go the wrong direction.
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#6
01-22-2013, 11:32 AM
 msh210 Non-Actuary Join Date: Jan 2013 Posts: 3

Quote:
 Originally Posted by Phileas Fogg I have one additional suggestion if you're doing the "hunt-and-peck"
Thanks!
#7
01-22-2013, 02:12 PM
 algebrat Member Non-Actuary Join Date: Nov 2012 Location: Ork Studying for GED Favorite beer: Scieoclean Posts: 2,143

Quote:
 Originally Posted by msh210 Thanks!
I second that, thanks Phileas
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#8
01-23-2013, 11:30 AM
 actuary-r Member SOA Join Date: Nov 2012 College: Abilene Christian University '13 Posts: 143

If you're on the fence about buying a financial calculator, here's one more reason to use a financial calculator on the exam: the BA 2 plus has a cash flow worksheet that can save you time (and possibly a mistake) if you have to find the present value of an uneven cashflow.
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