**By Sunil K. Parameswaran**

Mortgage loans are known as Amortized Loans. The equal instalments are computed for the remaining duration of the loan at the start of a period, typically the month. Most mortgage loans are repaid by way of equal periodic instalments at equally spaced intervals in time.

This is where the terms Equated Monthly Instalments (EMIs) comes from. Every payment will consist of an interest component and a principal component. Thus, outstanding principal and interest component of the instalment will decline with each instalment. However, since the instalment is fixed, the principal component will increase.

In practice, we have fixed rate and floating rate mortgages. In the case of the former the interest rate remains fixed for the duration of the loan. However, in the case of floating rate mortgages, the rates are typically reset at the beginning of every year. Whenever the rate is reset, the principal outstanding at that point of time will be re-amortized over the remaining term to maturity. If the interest rate has declined, so will the EMI. Else, if the interest rate has increased the EMI will go up.

One practical issue with loans is the possibility of a pre-payment. This is a principal payment at the end of the month that is over and above the scheduled principal. If the interest rate is constant, future EMIs will come down because of the prepayment, which serves to reduce the outstanding principal. In the case of a floating rate mortgage, the new EMI will be influenced by two factors, the unscheduled decline in the outstanding principal, and the new interest rate on the mortgage.

Pre-payment rates or pre-payment speeds are critical for projecting the cash flows from a mortgage loan. The Single Month Mortality or SMM is the percentage of the scheduled outstanding principal at the end of the month that is prepaid. Assume the outstanding amount at the beginning of the month is L. The interest rate is r% per month and the EMI is A. The principal component of the EMI is A-rL.

Thus the scheduled outstanding at the end of the month is L-(A-rL) = L(1+r)-A. If the SMM is m%, the prepayment for the month is m[L(1+r)-A]. Actual outstanding principal at month end is the scheduled outstanding minus the prepayment. The actual outstanding principal will then be re-amortized over the remaining term to maturity, based on the prevailing rate of interest. EMI for the next month, and its division into an interest component and a principal component, is based on actual principal at the beginning of the month. The scheduled principal at the end of the month is used solely for computing pre-payment amount at the end of the month.

The annual prepayment speed is called Conditional Pre-payment Rate (CPR). One minus the CPR is equivalent to one minus the SMM taken to the power of 12. Thus, that pre-paying at the rate of SMM 12 times a year is equivalent to pre-paying once at the end of the year at the CPR.

**The writer is CEO, Tarheel Consultancy Services**

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