Rule of 78, Hire Purchase

Car hire purchase for 3 years loan, 4.1% p.a. for MYR 27,000. If I want to settle my car loan one shot after the 16th payment, how much I had to pay for 17th payment and how much I had saved for the interest? Is the settlement worth to be executed? (assume FD = 3% p.a)

Let me introduce basic calculation in hire purchase. It is based sum of digit, or called as rule of 78.
One year monthly installment consists 12 months. Thus, if you add up at the number from 12nd to 1st numbers, it results 78. Sum of 12+11+10+9+8+7+6+5+4+3+2+1

= (12*(12+1))/2 = 78. Thus, it is also called as sum of digits.

Similarly, 2 years monthly installment, 3 years, 4 years, 5 years, 6 years, 7 years and 8 years results 300, 666, 1176, 1830, 2628, 3570 and 4656 respectively.

Term charges of the HP = Principle*interest*number of years
= 27000*0.041*3 = 3321.

Sum of digit = N*(N+1)/2
= 36*37/2 = 666.

Monthly installment = Principle+Term charges/(number of years*12)
= (27000+3321)/(3*12) = 842.25

For Rebate = n(n+1)*term charges/N(N+1)
= (36-16)*(36-16+1)*3321/(36*(36+1)) = 1047.16.

Outstanding installment = (36-16)*842.25 = 16845.
Thus, redemption sum = 16854 – 1047.16 = 15806.84.

Interest saving = Old HP – settled HP
= 842.25*36-(15806.84+16*842.25) = 1038.16.

Effective interest for old plan = 12*RATE(nper,pmt,pv,fv,type,guess)
= 12*RATE(36,-842.25,27000,0,0,0.15) = 7.692% p.a

Effective interest for old plan = using IRR from Cash flow see image = 7.515% p.a

Diverted original posting from my facebook note dated 21-Oct-09.