Question

Nine years ago a family incurred a 20-year RM90,000 mortgage at 8% effective on which they were making annual payments. They desire now to make a lump-sum payment of RM5000 and to pay off the mortgage in nine more years. Find an expression for the revised annual payment if the lender is satisfied with an 8% yield for the past nine years but insists on a 9% yield for the next nine years.

Answer 1

Formula for annual level payments is   I=[P*r*(1+r)^n]/[(1+r)^n-1]

Where I= Annual installment, P= Principal, r= Yearly interest rate and n=Period (number of yearly payments).

Yearly payments as per original plan= RM 9,166.70 as follows:

After 9 years, balance outstanding is the PV of future installments, calculated at RM 57,263.34 as follows:

Upon making lump sum payment of RM 5,000 revised principal for next 9 years= 57,263.34-5,000

= RM 52,263.34

Accordingly, the expression for annual payments for next 9 years at 9% interest is as follows:

52263.34*0.09(1+0.09)^9/[(1+0.09)^9 -1]

Annual payments of the loan for next 9 years= RM 8,717.46 as follows: