What is the interest rate compounded semi-annually?

Let's see if we tackle this problem:

1- The formula for calculating a loan or a mortgage payment is:

2- A. i(1 + i)^n /(1 +i)^n -1, where A=Amount of loan or morgage, i=Interest rate per period(monthly in this case), n=Total number of periods or(25 x 12=300 months)

3- In trying to find( i) directly by using this formula doesn't work. It's the same as trying ti find the yield on a Bond.

4- A method of "iteration" is used, basically a method of trial & error and then using successive approximations to find the right number.

5-By using this method, I was able to find a monthly interest rate of .4124%.

6-Since this is a monthy rate, will have to find semi-annual rate.

7- So we take this number & divide it by hundred and then add 1=1.004124

8- Then we compound it for 6 months as follows:(1.004124)^6=1.025

9-Then 1.025-1=.025 X 2=.05 X 100=5%. This is the NOMINAL rate compounded semi- annually. The effective annual rate would then be:        (1.025)^2=5.0625%. And that's your interest rate on your mortgage. And it checks out to be accurate.PHEW!!!!!!!!!!!!!!!. That was a good one!.

P.S. I forgot to mention that the monthly payments are made at the beginning of the month, which is rather unusual for a mortgage!. But there you have it.