Time Value of Money
Payback of a Loan with Fixed Capital Payments

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01:20 – Calculation of the Fixed Capital Payments
02:50 – First monthly payment
05:20 – Comparing the first monthly payments
07:20 – Second period
10:05 – Comparing the two methods
12:00 – Conclusion

In a previous video, we calculated the monthly payments of a loan or mortgage when we considered fixed monthly payments. We saw that every month the same amount is paid which is composed of the interest on the outstanding capital + a part of the capital. We saw that the outstanding capital is slowly decreasing as are the interest payments with as a result that the monthly payments of the capital are increasing.

In this new example, we will pay a fixed portion of the outstanding capital + the interest on the outstanding capital.
When we consider a loan of $150k over 30 years (360 monthly periods), the monthly amount of capital that is paid is equal to 150,000/360 = $417.67
And to this amount, we have to add the interest of 0.5% on the outstanding capital.

Let’s look at the first period:
Outstanding capital = $150,000
Interest on outstanding capital = 0.005 x 150,000 = $750
Total payment = 750 + 417.67 = $ 1,166.67 compared with the $899.33 with the other method
Capital remaining at the end of period 1
150,000 – 417.67 = $149,583.33 which is less than the capital at the end of the first period when we considered fixed monthly payments

Now the second period
Outstanding capital = $149,583.33
Interest on outstanding capital = 0.005 x 149,583.33 = $749.25
Total payment = 749.25 + 417.67 = $ 1,164.88 compared with the $899.33 with the other method
Capital remaining at the end of period 1
149,583.33 – 417.67 = $149,165.66 which is less than the capital at the end of the second period when we considered fixed monthly payments $149,701.34

Comparing the two methods
When we compare the two methods, we see that the second method results in a total lower cost of the loan and the total interest rate to be paid goes down from $173,757.28 to $135,375.00.
The disadvantage of the second period is that the initial payments are significantly higher than in the other case. It all depends on the possibilities that you have at the moment of closing the loan.

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