I am currently studying for the Exam FM for actuaries, and the calculator that I have is a TI 30X IIS, which was very helpful for me during the Exam P.
I cam as far as studying bonds, and the following is what I have been working on.
A 1000 par value bond pays annual coupons of 80. The bond is redeemable at par in 30 years, but is callable any time from the end of the 10th year at 1050. Based on her desired yield rate, an investor calculates the following potential purchase prices, $P$:
1), assuming the bond is called at the end of the 10th year, $P=957$
2), assuming the bond is held until maturity, $P=897$
The investor buys the bond at the highest price that guarantees she will receive at least her desired yield rate regardless of when the bond is called. The investor holds the bond for 20 years, after which time the bond is called. Calculate the annual yield rate the investor earns.
For this problem this is what I have so far.
1), $957 = 80a_{\overline{10}\rceil j}+1000v^{10}_j$
2), $897 = 80a_{\overline{30}\rceil j}+1000v^{30}_j$
It does not look like the problem is designed so that the present value factors $a_{\overline n \rceil}$ cancel out nicely, and yet this question came from the exam so I am wondering if a financial calculator is needed to solve this problem. I would love it if someone could tell me the following. (it would be most helpful if you have actually taken the Exam FM)
a), Is it possible to solve this problem with a basic scientific calculator? If so, how do we get rid of the annuity-present-value factor?
b), Is a financial calculator necessary for the Exam FM? I know that BA II+ is allowed for the exam and it seems like it is a financial calculator rather than a scientific one.
P.S.
I found that the yield rate can be calculated as $j=9\%$ from the first two information, but I am still having trouble finding the annual yield rate the investor earns.
The answer is supposedly $9.24\%$.
I think that the present value of the bond at $t=20$ is
$$P=80a_{\overline{20}\rceil .09}+1050(1.09)^{-20} \approx 917.64$$
so since the investor is purchasing the bond at the minimum yield which happens at the end of $t=30$, she buys it at $897$ so
$$897(1+i)^{20}=917.64(1.09)^{20}$$
which gives me $i \approx 9.12\%$
I used a plain Texas Instruments non-financial calculator for exam FM. The benefit of multiple choice problems is that there are a finite number of possible solutions. Once you've set up the correct equation, and you've discovered it's too hard to solve without numerical methods, you can just plug the different answers in and see which one works.
Since the expressions are usually either increasing or decreasing, you can also use binary search. You plug in a number that you think might be high, then one that you think is low, then plug in their average, and if that's too high then you plug in the average of the middle and the lower one, etc.