How do you calculate the rule of 78's?

Answer 1

RULE OF 78

Suppose you have a loan and find that you are able to pay it off early. How much interest should be returned to you? In your loan document, it will probably state that refunds would be based on the "Rule of 78."

Let's look at a example to see what this means.

Suppose you borrow $2000 at 6% and agree to pay it back in 12 monthly installments. According to the well-know formula for calculating the payment,

Payment =

Where P is the amount borrowed, i is the monthly interest rate and N is the number of payments.

We find that we would be told, on our loan document, that we would make 11 payments of $172.13 and a final payment of $172.17.

= 172.13

The extra 4 cents on the last payment is due to accumulated round off error.

Before looking at the Rule of 78, let's examine the amortization schedule for this loan.

AMORTIZATION SCHEDULE

Principle Payment Interest To Prin. New Balance

1. 2000.00 172.13 10.00 162.13 1837.87

2. 1837.87 172.13 9.19 162.94 1674.93

3. 1674.93 172.13 8.37 163.76 1511.17

4. 1511.17 172.13 7.56 164.57 1346.60

5. 1346.60 172.13 6.73 165.40 1181.20

6. 1181.20 172.13 5.91 166.22 1014.98

7. 1014.20 172.13 5.07 167.06 847.92

8. 847.92 172.13 4.24 167.89 680.03

9. 680.03 172.13 3.40 168.73 511.30

10. 511.30 172.13 2.56 169.57 341.73

11. 341.73 172.13 1.71 170.42 171.31

12. 171.31 172.17 .86 171.31 -0-

Now suppose, maybe because of a tax refund, you decide to pay off your loan two months early. If one looks at the amortization schedule, you would be saving the last two interest payments, $1.71 and .86 for a total of $2.57. However, the loan documents say that, in case you pay off early, the refund of interest will be according to the Rule of 78. Here's what that means. Since the loan was for 12 months, add the numbers from 1 - 12 (a little math). Now, 1 + 2 + … + 12 = 78. Hence the name! The interest on your loan is then divided into 78 shares. Your monthly payments total $2065.60, so the total interest would be $65.60. Divided by 78 yields $0.84 per share. Now the lender assumes it receives 12 shares of interest from your first payment ($10.08), 11 shares from your 2nd payment, etc. So, by paying off two months early, you save (1+2) =3 shares, for a total of $2.52. You lose $0.05!