## Sunday, April 21, 2013

### Rule of 78: What??? After one year payment why my loan principle not much different?

On first April last year you have bought a second hand car. You have make car loan for \$50000 with 7 years financing period. Interest rate for that loan is 5%. Your monthly installment is \$803.57.
On 1st April this year, suddenly you want to make full settlement because your company give you 24months salary bonus. You have checked with your car loan bank and find out you have pay \$45, 327.73 for full settlement.

Instead of check with your car loan bank, you also can estimate it using online full settlement calculator available in internet, In this case I will use online full settlement calculator from http://loanstreet.com.my.

The typical bank loan or Islamic financing using "Rule of 78" to calculate prepayment schedule and early  settlement rebate. Why it calls "rule of 78", it is sum of month number of the year  ( 1+2+3...+11+12 ) is 78. The earliest official use of the Rule of 78s to calculate the unearned portion of a loan’s finance charge was in Indiana in 1935.

You will  paying more interest in early repayment. From calculator above total rebate is RM12529.41. In Islamic financing, we call this rebate as Ibra'. The rebate above actually balance interest you should paid from settlement date until end of tenure.

Total rebate based on Rule of 78 formula is =  f *( k(k+1) )/ n(n+1) ),
where  f = total agreed finance charges; k = number of months paying off early( remaining months to pay); n = total term of loan in months.

Early settlement amount,
= Initial loan amount - instalments already paid + total interest - interest rebate (rule of 78) + penalty (a percentage of the interest rebate).

From repayment schedule above which I generate from http://www.drcalculator.com/calc/rule78.cgi , we can straightway pick interest rebate from "Interest left to Pay" on month 13.

The magic number in the table calculate using formula
=  ( total term of loan in months/ 2 ) * ( total term of loan in months  + 1 )
=( 84/2) * (84+1)
= 3570

This number will use to calculate interest portion for every month by using following formula:
= total interest * ( ( total term of loan in months- total month instalments already paid ) /  magic number )

For first month the interest paid is,

= 17500 * ( ( 84-0 )/3570 )
=411.76

This is why when you do early settlement too early, the settlement amount not much different from your  total loan.

This is also why bank so happy when you refinance or overlapped the amount. When you this, the interest portion will back same as month one.