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Minsk · 10-31-2007, 08:02 PM

Compare and contrast the actuarial method and the Rule of 78s method for determining interest savings.?

taxguru · 10-31-2007, 08:02 PM

The actuarial method is going to be exact. The actuarial method can be a monthly or daily calculation. The Rule of 78s is an approximation based on a full number of months.

From my little analysis I just did, it looks like the approximation gets worse the higher the interest rate (I tried 1%, 3%, 5% 10% & 25%). 10% & 25% didn't work well, IMO, but the others did. The analysis was based on monthly calculations.

If I did an exact number of days calculation the rule of 78s wouldn't work well at all because it is based on a full number of months.

briansol · 08-07-2008, 06:50 AM

from wikipedia:

Quote:

Overview

Also known as the sum-of-the-digits method, the Rule of 78s is a term used in lending that refers to a method of yearly interest calculation. The name comes from the total number of months' interest that is being calculated in a year (the first month is 1 month's interest, whereas the second month contains 2 months' interest, etc.). This is an accurate interest model only based on the assumption that the borrower pays only the amount due each month. If the borrower pays off the loan early, this method maximizes the amount paid by applying funds to interest before principal.
A simple fraction (as with 12/78) consists of a numerator (the top number, 12 in the example) and a denominator (the bottom number, 78s in the example). The denominator of a Rule of 78s’ loan is the sum of the digits, the sum of the number of monthly payments in the loan. For a 12 month loan, the sum of numbers from 1 to 12 is 78 (1 + 2 + 3 + . . . +12 = 78). For a 24 month loan, the denominator is 300. The sum of the numbers from 1 to n is given by the equation n (n+1) / 2. If n were 24, the sum of the numbers from 1 to 24 is 24 (24+1) / 2 = 12 x 25 = 300, which is the loan’s denominator, D.
For a 12 month loan, 12/78s of the finance charge is assessed as the first month’s portion of the finance charge, 11/78s of the finance charge is assessed as the second month’s portion of the finance charge and so on until the 12th month at which time 1/78s of the finance charge is assessed as that month’s portion of the finance charge. Following the same pattern, 24/300 of the finance charge is assessed as the first month’s portion of a 24 month precomputed loan.

Formula for calculating the unearned interest:

u = f X k(k+1)/n(n+1)

u = unearned interest;
f = total agreed finance charges;
k = number of months paying off early;
n = total term of loan in months

Basically, it's a way to pad interest and was originally conceited in the early days before calculators to calculate payoffs for loans when more than the base payment was made (ie, additional principal)

It should be avoided. It makes the lender money, not you.

10-31-2007, 08:02 PM	#1 (permalink)
Minsk Greenhorn Join Date: Jul 2006 Posts: 16 Rep Power: 0	Compare and contrast the actuarial method and the Rule of 78s method for determining interest savings.? Compare and contrast the actuarial method and the Rule of 78s method for determining interest savings.?

10-31-2007, 08:02 PM	#2 (permalink)
taxguru Greenhorn Join Date: Jul 2006 Posts: 29 Rep Power: 3	Compare and contrast the actuarial method and the Rule of 78s method for determining interest savings.? The actuarial method is going to be exact. The actuarial method can be a monthly or daily calculation. The Rule of 78s is an approximation based on a full number of months. From my little analysis I just did, it looks like the approximation gets worse the higher the interest rate (I tried 1%, 3%, 5% 10% & 25%). 10% & 25% didn't work well, IMO, but the others did. The analysis was based on monthly calculations. If I did an exact number of days calculation the rule of 78s wouldn't work well at all because it is based on a full number of months. Last edited by briansol; 08-07-2008 at 06:42 AM.

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