<PRE><B>Question 1133470</B>
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The answer from tutor @MathLover1 is not the way loans work.  Her method is to say that immediately upon taking out the loan, the amount you owe is equal to all 360 monthly payments of $1,393.70, and the amount you owe decreases linearly until the balance is 0 after 360 months.&lt;br&gt;
The answer from tutor @MathTherapy shows the right answers, and shows a formula you can use for calculating the remaining amount of the loan at any time.&lt;br&gt;
But that formula is awkward; and you need to use the formula with new inputs each time you calculate the remaining amount after a certain number of payments.&lt;br&gt;
It is much easier to use a spreadsheet like excel to see exactly how the loan is amortized; you will be able to see immediately the amount remaining after each payment.&lt;br&gt;
If you aren&#39;t familiar with spreadsheets, you should get familiar with them -- they are extremely useful for many kinds of problems; loan amortization is an excellent example.&lt;br&gt;
Here&#39;s how you can create the amortization table using excel.&lt;br&gt;
(1) Put the initial loan amount in cell A1.  Column A is going to show the remaining loan amount at the beginning of each month, before a payment is made.&lt;br&gt;
(2) In cell B1, enter &quot;=A1*(1+.042/12)&quot;.  This will multiply the number in cell A1 (the beginning amount of the loan) by the monthly growth factor, based on the annual 4.2% interest rate.  So the entries in column B are going to be the amounts remaining on the loan, after interest has been added, but before a payment has been made.&lt;br&gt;
(3) In cell C1, enter &quot;=B1-13993.70&quot;.  This will subtract a loan payment, yielding the amount remaining on the loan after the first payment.  So the entries in column C will be the amounts remaining on the loan right after a payment is made.&lt;br&gt;
(4) In cell A2, enter &quot;=C1&quot;.  This will copy the number in cell C1 (the amount remaining after the first payment), making it the amount remaining on the loan at the beginning of the second month.&lt;br&gt;
(5) Then copy the entries in cells B1 and C1 to cells B2 and C2.  Copying in this way in excel will make the new columns perform the same calculations as the old columns.  So doing this will make cell B2 contain the amount remaining on the loan after interest has been added for the second month; and it will make cell C2 contain the remaining balance after the second payment has been made.&lt;br&gt;
One way to do the copy in excel is to highlight cells B1, C1, B2, and C2 and type control-D.&lt;br&gt;
(6) Then copy the entries in cells A2, B2, and C2 in their respective columns to row 360.  Again you can do this by highlighting columns A, B, and C from row 2 to row 360 and typing control-D.&lt;br&gt;
The entries in column C will show the amounts remaining on the loan after each payment.  If you have entered everything correctly, you will see the loan balance goes from positive to negative after month 360.&lt;br&gt;
Now it will be easy to read off the amounts remaining on the loan after 10 years (120 payment), 15 years (180 payments), and 25 years (300 payments).</PRE>