Add on Interest
When a consumer loan is made with an add-on interest rate, the interest for the entire term of the loan is calculated at the start of the loan by the equation:
where:
I = total interest
P = principal
R = annual interest rate
T = term in years
Example
A bank loaned $11,025 at an interest rate of 8.8435% to be repaid in 12 equal monthly installments. The dollar amount of the interest as calculated by the equation above is $975.The periodic payment on an add-on interest loan is calculated by the equation:
where:
Pmt = payment
P = principal
I = total interest (as calculated above)
n = total number of payments
Example
The principal of $11,025 is added to the calculated interest of $975 to get $12,000. When this is divided by 12 monthly installments, the result is a monthly payment of $1,000.The important point about an add-on interest rate is the difference between the stated, or quoted, interest rate and the annual percentage yield, which may be almost twice the stated interest rate. The reason for the difference is that the interest is calculated on the full principal amount over the life of the loan, when in fact, part of the principal is being reduced with each periodic payment.
Once the amount of each payment has been determined, interest and principal payments will be billed during each payment period. The amount of principal billed is simply the total payment minus the interest billed. The amount of interest billed is calculated by the rule of 78s.
The rule of 78s uses the sum of the digits of the total number of payments.
Example
In our 12 month loan, the sum of the digits is:12 + 11 + 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 78
The sum of the number of digits may be calculated for loans of any length by using the formula:
where:
n = the number of periods
Example
Next, the total calculated interest is divided by the sum of the digits to determine a value of interest per digit.
Example
The portion of each payment that is interest is calculated as follows:
For the first payment, the interest per digit is multiplied by the total number of payments.
For each subsequent payment, the multiplier is one less than in the previous payment, until the final payment, in which the multiplier will be 1.
This will result in all of the calculated interest being billed by the end of the loan.
Example
|
Month |
Number of Digits |
Interest per Digit |
Interest per Month |
|---|---|---|---|
|
1 |
12 |
$12.50 |
$150.00 |
|
2 |
11 |
$12.50 |
$137.50 |
|
3 |
10 |
$12.50 |
$125.00 |
|
4 |
9 |
$12.50 |
$112.50 |
|
5 |
8 |
$12.50 |
$100.00 |
|
6 |
7 |
$12.50 |
$87.50 |
|
7 |
6 |
$12.50 |
$75.00 |
|
8 |
5 |
$12.50 |
$62.50 |
|
9 |
4 |
$12.50 |
$50.00 |
|
10 |
3 |
$12.50 |
$37.50 |
|
11 |
2 |
$12.50 |
$25.00 |
|
12 |
1 |
$12.50 |
$12.50 |
|
Totals |
78 |
|
$975.00 |
Because the Nortridge Loan System does all accrual posting on a daily basis, the system will divide the current period’s calculated interest by the number of days in the current period to determine the current per diem.
Example
If month #1 is assumed to be January in the example above, our per diem for each month is calculated as follows:Month | Interest per Month | Days in the Month | Per Diem Interest |
|---|---|---|---|
January | $150.00 | 31 | $4.83871 |
February | $137.50 | 28 | $4.91071 |
March | $125.00 | 31 | $4.03226 |
April | $112.50 | 30 | $3.75000 |
May | $100.00 | 31 | $3.22581 |
June | $87.50 | 30 | $2.91667 |
July | $75.00 | 31 | $2.41935 |
August | $62.50 | 31 | $2.01613 |
September | $50.00 | 30 | $1.66667 |
October | $37.50 | 31 | $1.20968 |
November | $25.00 | 30 | $0.83333 |
December | $12.50 | 31 | $0.40323 |
