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# Loan Payment...

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A loan for \$150,000 for 30 years at 6% compounded semi-annually. What is the monthly payment of this loan and at what payment will the loan be reduced to approximately \$75,000, or about half the original principal? Thank you for help.

Apr 19, 2018

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The first thing you have to do is to convert 6% from compounded semi-annually to compounded monthly. And you can do that as follows:

1.03^(1/6) =1.004938622 - 1 x 100 =0.4938622% - This is the monthly compound rate.

0.4938622 x 12 =5.9263464% - This is the annual rate compounded monthly.

I shall use this amortization schedule to give you all the answers you want:

http://www.calculator.net/amortization-calculator.html?cloanamount=150000&cloanterm=30&cinterestrate=5.9263464&printit=0&x=55&y=25

All the answers to your question are in the above amortization schedule:

Look at the top and you will see the monthly payment = \$892.24

Look at the last column of the table where it says "Ending Balance". Go down that column until you see a balance closest to \$75,000, and, quickly, you will see that after the 251st payment the balance of the loan will be =\$75,064.79, which the closest to \$75,000 as you can get.