Cash Equivalency Example #2
We'll use our prior ITAO example for another problem. Let's say we wanted to find out what the separate loan principal and interest amounts were for the first monthly payment.

Vm or Mortgage = $80,000

Ym or Interest Rate = 12%

n or Term = 30 year payment term (amortization)
Using the ITAO tables for the 30 year term we found the correct monthly loan payment amount:
$80,000 x 0.010286 = $822.88
We need to figure what amount of the $822.88 first monthly payment is applied toward loan principal and what amount is toward loan interest. To do this we first need to find the monthly interest rate. The nominal interest rate is given to us as 12%. The monthly interest rate is simply the nominal rate divided by 12.
.12/12 = .01 or 1% interest per month
The total loan principal amount for the first monthly payment is given to us as $80,000. If the monthly interest rate is 1%, we then multiply this by the outstanding loan principal amount to determine what the interest payment is, for that particular monthly payment.
$80,000 x .01 = $800.00
Now we have found the interest payment for the first month to be $800.00. All we need to do is subtract this amount from the total monthly loan payment to figure out the loan principal amount for that month.
$822.88  $800.00 = $22.88
The amortization of the loan principal or the recapture of capital for the first monthly loan payment is $22.88. This may seem surprisingly low, but I noted the reason for this earlier. The vast majority of the loan payments made in the early years are applied toward paying down the loan interest balance, instead of the loan principal balance.
We'll use this same example for another problem. Let's say we wanted to find what the remaining loan principal balance is after the first year of loan payments. As shown in prior examples, we can do this two ways, using either the ITAO column figure or the Rm column figure. First we find the ITAO figure for a 12% interest loan at the 29 year term is 0.010324. Since we are using the monthly ITAO, then we must use the monthly loan payment to find the remaining loan principal amount.
$822.88/0.010324 = $79,705.54
Or we can find that the Rm figure for a 12% interest loan at the 29 year term is 0.123888. Since we are using the yearly Rm, then we must use the yearly loan payment to determine the loan principal amount.
$9,874.56/0.123888 = $79,705.54
Using both methods, we come up with the same answer. The loan principal balance that is outstanding after 1 year of loan payments will be $79,705.54.
We can figure out the amount of loan principal paid during the first year of loan payments. To do this, we simply subtract the original loan principal amount from the remaining amount after 1 year of payments.
$80,000  $79,705.54 = $294.46
The amortization of the loan principal, or the recapture of capital, after the first year of loan payments is $294.46.
We'll use this same example to see how the loan amortizes over 5 year intervals. Let's say we wanted to determine what the remaining loan principal balance is after 10 years of loan payments. As shown in prior examples, we can do this two ways, using either the ITAO column figure or the Rm column figure.
First we find that the ITAO figure for a 12% interest loan at the 20 year term is 0.011011. Since we are using the monthly ITAO, then we must use the monthly loan payment to find out the remaining loan principal amount.
$822.88/0.011011 = $74,732.54
Or we can find that the Rm figure for a 12% interest loan at the 20 year term is 0.132132. Since we are using the yearly Rm, then we must use the yearly loan payment to determine the loan principal amount.
$9,874.56/0.132132 = $74,732.54
Using both methods, we come up with the same answer. The loan principal balance that is outstanding after 10 years of loan payments will be $74,732.54.
We can determine the amount of loan principal paid during the first 10 years of loan payments. Simply subtract the original loan principal amount from the remaining amount after 10 years of payments.
$80,000  $74,732.54 = $5,267.46
(Yes, we're going to keep practicing it until you can do this in your sleep!) Now we'll learn what the remaining loan principal balance is after 15 years of loan payments.
First we find that the ITAO figure for a 12% interest loan at the 15 year term is 0.012002.
$822.88/0.012002 = $68,561.91
Or we can find that the Rm figure for a 12% interest loan at the 15 year term is 0.144024.
$9,874.56/0.144024 = $68,561.91
Using both methods, we come up with the same answer. The loan principal balance that is outstanding after 15 years of loan payments will be $68,561.91.
Now we'll find out what the remaining loan principal balance is after 20 years of loan payments.
First we find that the ITAO figure for a 12% interest loan at the 10 year term is 0.014347.
$822.88/0.014347 = $57,355.54
Or we can find that the Rm figure for a 12% interest loan at the 10 year term is 0.172164.
$9,874.56/0.172164 = $57,355.54
Using both methods, we come up with the same answer. The loan principal balance that is outstanding after 20 years of loan payments will be $57,355.54.
(OK, this is the last one  practice makes perfect!) Now we'll learn what the remaining loan principal balance is after 25 years of loan payments.
First we find that the ITAO figure for a 12% interest loan at the 5 year term is 0.022244.
$822.88/0.022244 = $36,993.35
Or we can find that the Rm figure for a 12% interest loan at the 5 year term is 0.266928.
$9,874.56/0.266928 = $36,993.35
Using both methods, we come up with the same answer. The loan principal balance that is outstanding after 25 years of loan payments will be $36,993.35.