
Mortgage
A couple buys a home and signs a mortgage contract for $200,000 to be paid with monthly payments over a 25year period at i^(2) = 0.04.
What is the monthly payment?
n=25*12
The confusing part for me is the interest rate, how do I know which one to use?
I'm thinking I have to convert i^(2) to i^(12) then use j=i^(12)/12.
Is there a quick relationship I can use to convert the interest rate? Currently I'm converting i^(2) to annual interest rate then back to i^(12)
K* annuity(n)j = 200 000 and solve for K

Re: Mortgage
Assuming i^(2) means your rate per period, which is twice a year, that would mean your $\displaystyle j_{2}$ rate = 8%.
You need to use an interest rate that is compounded with the same frequency as your regular payments.
To convert from a semiannual (twice a year) interest rate, to an equivalent monthly interest rate simply set up the following equation:
$\displaystyle (1+\frac{0.08}{2})^2 = (1+\frac{j_{12}}{12})^{12}$
solving for $\displaystyle j_{12}$:
$\displaystyle (1.04)^{\frac{2}{12}}=1+\frac{j{12}}{12}$
$\displaystyle j_{12} = 12\times ((1.02)^{\frac{2}{12}}1)$
$\displaystyle = 7.869836324$%
A good way to check that you have calculated the new interest rate correctly is to compare it to your original one. Because monthly rates compound more often than semiannual rates, in order for the two to be equal as an annual rate, the monthly rate should be slightly less than the 8% rate used when compounding twice a year.
$\displaystyle j_{12} = 7.869836324$% which is slightly less than 8%
Remember that the 8% and 7.869836324% are the annual rates so divide by the number of time periods before you use them. The monthly interest rate you will be using for your loan repayments will be $\displaystyle \frac{7.869836324}{12}$. Also, make sure to use your calculator and store the value you get for your interest rate  don't ever round it off.