5.1 Basics
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Problem. To purchase a house, you take out a 30 year mortgage. The present value (loan amount) of the
mortgage is $300,000. The mortgage charges an interest rate / year of 8.00%. What is the annual payment
required by this mortgage? How much of each year's payment goes to paying interest and how much
reducing the principal balance?
Solution Strategy. First, we use Excel’s PMT function to calculate the annual payment of a 30 year
annuity (mortgage). Then we will use a time line and simple recursive formulas to split out the payment
into the interest component and the principal reduction component.
FIGURE 5.1 Spreadsheet for Loan Amortization - Basics.
How To Build Your Own Spreadsheet Model.
1. Inputs. Enter the inputs in the range B4:AF9.
2. Year and Freeze Panes. Enter 1, 2, 3, …, 31. in the range B9:G11. A simple way to do this is to
enter 1 in cell B9, enter 2 in cell C9, hover the cursor over the lower right corner of cell C9, and
when you see the "fill handle" (it looks a "+" sign) drag it all the way across to cell G11. Select
C10 and click on Window | Freeze Panes. This locks in the column and row titles.
3. Beg. Principal Balance. The principal balance at the beginning of Year 1 is the full amount of
the loan (i.e., the present value). Enter =B4 in cell B10. We will return to the rest of this line in a
moment.
4. Payment. The Excel PMT function can be used to calculate an annuity payment using the
following format =PMT(Interest Rate / Year, Number of Years, -Present Value, 0). Enter
=PMT($B$5,$B$6,-$B$4,0) in cell B11. The $ signs in the formula lock in the row and column
when copying.
5. Interest Component in year t = (Interest rate/year) * (Beginning Principal Balance in year t).
Enter =$B$5*B10 in cell B12.
6. Principal Component in year t = Payment - (Interest Component). In other words, whatever
part of the payment is leftover after paying the interest goes to reducing the principal balance.
Enter =B11-B12 in cell B13.
7. Beg. Principal Balance in year t = (Beg. Principal Balance in year t-1) - (Principal Component
in year t-1). Enter =B10-B13 in cell C10
8. Copy The Formulas. Select the range B11:B13 and copy it to C11. Select the range C10:C13
and copy it to the range D10:AE10. Select the cell AE10 and copy it to AF10.
The Annual Payment is $26,648. Figure 2 shows the final years of the time line for the loan.
FIGURE 5.2 Final Years of the Time Line of Loan Amortization - Basics.
The principal balance drops to zero in year 31 after the final payment is made in year 30. The loan is paid
off! It doesn't matter whether the zero amount in cell AF10 displays as positive or negative. The only
reason it would display as negative is due to round off error in the eighth decimal or higher, which is
irrelevant of our purposes.
The Interest Component depends on the size of the Beg. Principal Balance. In year 1 the interest
component starts at its highest level of $24,000 because the Beg. Principal Balance is at its highest level
of $300,000. The interest component gradually declines over time as the Principal Balance gradually
declines over time. The interest component reaches its lowest level of $1,974 as the Beg. Principal
Balance reaches its lowest level of $300,000. The principal repayment component is the residual part of
the payment that is left over after the interest component is paid off. In year 1 when the interest
component is the highest, the principal component is the lowest. Even though you made a payment of
$26,648 in year 1, only $2,648 of it went to paying off the principal! The principal payment gradually
increases over time until it reaches its highest level of $24,674 in year 30.
Problem. To purchase a house, you take out a 30 year mortgage. The present value (loan amount) of the
mortgage is $300,000. The mortgage charges an interest rate / year of 8.00%. What is the annual payment
required by this mortgage? How much of each year's payment goes to paying interest and how much
reducing the principal balance?
Solution Strategy. First, we use Excel’s PMT function to calculate the annual payment of a 30 year
annuity (mortgage). Then we will use a time line and simple recursive formulas to split out the payment
into the interest component and the principal reduction component.
FIGURE 5.1 Spreadsheet for Loan Amortization - Basics.
How To Build Your Own Spreadsheet Model.
1. Inputs. Enter the inputs in the range B4:AF9.
2. Year and Freeze Panes. Enter 1, 2, 3, …, 31. in the range B9:G11. A simple way to do this is to
enter 1 in cell B9, enter 2 in cell C9, hover the cursor over the lower right corner of cell C9, and
when you see the "fill handle" (it looks a "+" sign) drag it all the way across to cell G11. Select
C10 and click on Window | Freeze Panes. This locks in the column and row titles.
3. Beg. Principal Balance. The principal balance at the beginning of Year 1 is the full amount of
the loan (i.e., the present value). Enter =B4 in cell B10. We will return to the rest of this line in a
moment.
4. Payment. The Excel PMT function can be used to calculate an annuity payment using the
following format =PMT(Interest Rate / Year, Number of Years, -Present Value, 0). Enter
=PMT($B$5,$B$6,-$B$4,0) in cell B11. The $ signs in the formula lock in the row and column
when copying.
5. Interest Component in year t = (Interest rate/year) * (Beginning Principal Balance in year t).
Enter =$B$5*B10 in cell B12.
6. Principal Component in year t = Payment - (Interest Component). In other words, whatever
part of the payment is leftover after paying the interest goes to reducing the principal balance.
Enter =B11-B12 in cell B13.
7. Beg. Principal Balance in year t = (Beg. Principal Balance in year t-1) - (Principal Component
in year t-1). Enter =B10-B13 in cell C10
8. Copy The Formulas. Select the range B11:B13 and copy it to C11. Select the range C10:C13
and copy it to the range D10:AE10. Select the cell AE10 and copy it to AF10.
The Annual Payment is $26,648. Figure 2 shows the final years of the time line for the loan.
FIGURE 5.2 Final Years of the Time Line of Loan Amortization - Basics.
The principal balance drops to zero in year 31 after the final payment is made in year 30. The loan is paid
off! It doesn't matter whether the zero amount in cell AF10 displays as positive or negative. The only
reason it would display as negative is due to round off error in the eighth decimal or higher, which is
irrelevant of our purposes.
The Interest Component depends on the size of the Beg. Principal Balance. In year 1 the interest
component starts at its highest level of $24,000 because the Beg. Principal Balance is at its highest level
of $300,000. The interest component gradually declines over time as the Principal Balance gradually
declines over time. The interest component reaches its lowest level of $1,974 as the Beg. Principal
Balance reaches its lowest level of $300,000. The principal repayment component is the residual part of
the payment that is left over after the interest component is paid off. In year 1 when the interest
component is the highest, the principal component is the lowest. Even though you made a payment of
$26,648 in year 1, only $2,648 of it went to paying off the principal! The principal payment gradually
increases over time until it reaches its highest level of $24,674 in year 30.