# Can Someone Explain the Rule of 78?

D

#### DarkProtoman

How exactly did they calculate this:

Guy gets a \$20000 loan at 8% annually for 60 months
Wins lottery and pays it off in 6 months.
Lender gives him a rebate that turns out to be \$44 less then he
should've gotten, by using the rule of 78.

Here the article:
http://www.bankrate.com/brm/news/dollardiva/19991012a.asp

I don't quite get the rule of 78. How did they calculate the rebate?
What IS the rebate? This article leaves me with more questions than

S

#### Steve

DarkProtoman said:
How exactly did they calculate this:

Guy gets a \$20000 loan at 8% annually for 60 months
Wins lottery and pays it off in 6 months.
Lender gives him a rebate that turns out to be \$44 less then he
should've gotten, by using the rule of 78.

Here the article:
http://www.bankrate.com/brm/news/dollardiva/19991012a.asp

I don't quite get the rule of 78. How did they calculate the rebate?
What IS the rebate? This article leaves me with more questions than
If you google "rule of 78" the first explanation is pretty good

..

--

D

#### DarkProtoman

Steve said:
If you google "rule of 78" the first explanation is pretty good
That didn't quite explain it. Like, if I pay off a \$1000 loan at 8.25%
monthly with a term of 24 months in only 12 months, how do they calc
the prepayment penalty?

R

#### Rusty

That didn't quite explain it. Like, if I pay off a \$1000 loan at 8.25%
monthly with a term of 24 months in only 12 months, how do they calc
the prepayment penalty?
With a simple interest loan (aka flat interest rate) the loan account is
charged with the full amount of interest at the beginning of the loan.
Unlike a reducing interest loan where the interest is charged each month.

When you wish to pay out a simple interest loan early, the interest rebate
is calculated using the rule of 78 as explained in the article referred to.
One point to remember, a simple interest rate of 8% over five years works
out to around 14% reducible monthly.

So, a penalty is not being calculated as such, it just happens to be the
difference between the two ways of working out the final payment.

Hope this helps,
Rusty

D

#### DarkProtoman

Rusty said:
With a simple interest loan (aka flat interest rate) the loan account is
charged with the full amount of interest at the beginning of the loan.
Unlike a reducing interest loan where the interest is charged each month.

When you wish to pay out a simple interest loan early, the interest rebate
is calculated using the rule of 78 as explained in the article referred to.
One point to remember, a simple interest rate of 8% over five years works
out to around 14% reducible monthly.

So, a penalty is not being calculated as such, it just happens to be the
difference between the two ways of working out the final payment.

Hope this helps,
Rusty
But the loan is precomputed. Please write out the steps to arrive to
the rebate. Thanks!!!!

P

#### Peter Saxton

But the loan is precomputed. Please write out the steps to arrive to
the rebate. Thanks!!!!
Post your calculations and I'll tell you what's wrong.

D

#### DarkProtoman

Peter said:
Post your calculations and I'll tell you what's wrong.
Rule of 78 method
------------------------------------------------------
\$24331.80 *(\$405.53*6)=\$21898.62
\$21898.62-\$20000=\$1898.62
\$1898.62-\$816.65=\$1081.97

Normal Method
--------------------------------------------------------
\$24331.80*(\$405.53*6)=\$21898.62
\$21898.62-\$20000=\$1898.62
\$1898.62-\$772.57=\$1126.05

Difference b/w the two methods: \$44.08

Can you check this? Thanks!!!!

P

#### Peter Saxton

Rule of 78 method
------------------------------------------------------
\$24331.80 *(\$405.53*6)=\$21898.62
\$21898.62-\$20000=\$1898.62
\$1898.62-\$816.65=\$1081.97

Normal Method
--------------------------------------------------------
\$24331.80*(\$405.53*6)=\$21898.62
\$21898.62-\$20000=\$1898.62
\$1898.62-\$772.57=\$1126.05

Difference b/w the two methods: \$44.08

Can you check this? Thanks!!!!

Write the calculations down and post them.

D

#### DarkProtoman

Peter said:

Write the calculations down and post them.
But these ARE all of them. Do you want the values I summed for \$816.65
and \$772.57?

\$816.65=(60/1830)*\$4331.80+(59/1830)*\$4331.80+(58/1830)*\$4331.80+...+(55/1830)*\$4331.80=(345/1830)*\$4331.80
(6 months interest from rule of 78 method)

\$772.57=\$133.34+\$131.52+\$129.70+\$127.86+\$126.01+\$124.14 (6 months
interest calculated normally)

Does this help?

P

#### Peter Saxton

But these ARE all of them. Do you want the values I summed for \$816.65
and \$772.57?

\$816.65=(60/1830)*\$4331.80+(59/1830)*\$4331.80+(58/1830)*\$4331.80+...+(55/1830)*\$4331.80=(345/1830)*\$4331.80
(6 months interest from rule of 78 method)

\$772.57=\$133.34+\$131.52+\$129.70+\$127.86+\$126.01+\$124.14 (6 months
interest calculated normally)

Does this help?
Didn't you have to do the full calculation to check the first
calculation was correct?

In the second calculation you haven't explained the calculation behind
each number.

D

#### DarkProtoman

Peter said:
Didn't you have to do the full calculation to check the first
calculation was correct?

In the second calculation you haven't explained the calculation behind
each number.
I got the numbers from a amortization calculator, OK. I then added up
the interest paid each month to arrive at the number I subtracted from
\$24331.80-(405.53*6)=\$21898.62. Here's the calculators:

Rule of 78: http://www.hughchou.org/calc/rule78.cgi
Normal: http://www.hughchou.org/calc/genloan.cgi

D

#### DarkProtoman

Peter said:
You said the loan was for a term of 24 months but the calculations you
did were only for 12 months.
Try entering in the amounts it asks for. That was for the original
question. Oh, and here's the difference for \$1000 at 8.25% monthly for
24 months, that's paid off in 6 months.

Rule of 78: \$174.73
Normal: \$270.43
Diff: \$95.70

P

#### Peter Saxton

Try entering in the amounts it asks for. That was for the original
question. Oh, and here's the difference for \$1000 at 8.25% monthly for
24 months, that's paid off in 6 months.

Rule of 78: \$174.73
Normal: \$270.43
Diff: \$95.70
Why did you use 60 in the first calculation?

D

#### DarkProtoman

Peter said:
Why did you use 60 in the first calculation?
The term was 60 months, or 5 years.