In order to understand how the BA II+ works, I would like to know the algebraic representation of it.
For example, for the problem below
Present value of an annual coupon bond that pays 80 per year is 897. The bond is called in 20 years where the redemption value is 1050. Calculate the annual effective interest rate.
Algebraically speaking it is a pretty simple expression;
$$897=80a_{\overline {20}\rceil i}+1050v^{20}$$
where $i$ is the interest rate and $v=(1+i)^{-1}$.
The problem solution tells me to use a financial calculator to solve for this, and I get it, it is a 21 degree polynomial which would be hopeless to solve by hand, and my goal is to learn how to use my BA II+ to solve for this.
What I know so far is to calculate rates for loans, for example,
A loan of $1000$ is made for 10 years at an interest rate of $5\%$ per annum. If the loan is paid off at a level payment $K$, $K=$
This is equivalent to
$$Ka_{\overline{10}\rceil .05}=1000$$
and on BA II+ I would do... $FV =0, \ PV = 1000, \ I/Y=10, \ N=10$ and $CPT PMT$ to find $K$.
How would it work with bonds, though?
What I would like to say so far is that
$$PV = Fra_{\overline{n}\rceil i}+Cv^{n}$$
so I think I know what $PV,\ N$ and $I/Y$ should be, but I am not sure what $FV$ and $PMT$ would be?
Any help would be great :)
It turns out, that the BA II + uses the following eqn.
$$PV+PMTa_{\overline{n}\rceil i}+FVv^{n}=0$$
So, it makes sence that the Payment must be a negative value when calculated.
It is useful especially for interest calculations, which often involves polynomials of high degrees when tried to be solved manually.
The instant calculation of Time Value of Money is a great advantage regarding exams, although the "blindness" of what you have plugged in in the calculator can be an obstacle.