Amortisation of Loans A loan repayment can be thought of as consisting of two components: (1) interest on the outstanding loan (2) repayment of part of the loan This perspective of loan repayment is called amortisation. The key to this process is the fact that the principal outstanding is the present value of the remaining payments.

Example Consider the following loan: $5000 over 5 years at 12% compounded monthly. Monthly repayment:

The interest component of this payment will change (decrease) as repayments are made.

For the first payment, The principal outstanding at the beginning of the period is $5000. :. Interest charged in that period Payment $ Interest $50 Part repayment $61.22

After 3 years, (which is 36 repayments) The principal outstanding is given by 24 payments are yet to be made.

So interest charged leaving as part repayment from the principal.

At the beginning of the last period: The principal outstanding is The interest charged for the period will be and will “pay out” the remaining principal.

The total interest paid (sometimes called the finance charge) A table showing the repayment analysis is called an amortisation schedule.

Amortisation schedule

Example 1 A loan of $70000 is to be repaid by monthly payments of $900. How long will it take to repay the loan at 14% compounded monthly?

The loan would be repaid in months (206 months, the last repayment < $900). This is equivalent to 17 years 2 months

Example 2: Finance charge Suppose you have the choice of taking out an $80000 mortgage at 12% compounded monthly for either 15 years or 30 years. How much saving is there in the finance charge if you were to choose the 15-year mortgage? Principal = Taken over 15 years,

So and Total interest is given by:

2. Taken over 30 years Total interest is given by:

Interest over 15 years $ Interest over 30 years $ Interest saved by taking the loan over the shorter time Taking the loan over 30 years has the advantage of lower repayments but much more money is repaid in total.

Example 3 A loan of $2000 is being amortised over 48 months at an interest rate of 12% compounded monthly. Find: (a)the monthly payment (b)the principal outstanding at the beginning of the 36 th month (c)the interest in the 36 th payment (d)the principal in the 36 th payment (e)the total interest paid.

(a) the monthly payment Monthly repayments are $52.67

b)The principal outstanding at the beginning of the 36 th month. At the beginning of the 36 th period there are 13 payments remaining The outstanding principal is $639.08

(c) Interest in the 36 th payment will be (d) the principal repaid in the 36 th repayment (e) the total interest is given by