FM for Actuaries

5
Loans and
Costs of Borrowing
Loans are usually paid back by periodic installments. Upon payment
of the installments, the balance of the loan reduces. We introduce
two methods of calculating the balance of the loan, namely, the
prospective method and the retrospective method. The two methods
are mathematically equivalent.
The quantum of each installment can be determined by the amortization
method or the sinking fund method. In the amortization method,
each installment is used to offset the interest incurred over the period
and to reduce the principal. For the sinking fund method, installments
are made up of a portion used to offset the interest and another portion
used to accumulate an amount to repay the principal. We extend
our analysis to installments that are of unequal amounts, as well as
to the case where interest rates are varying.
Lending and borrowing serve an important function in varying a person’s
consumption pattern and timing. The quoted rate of interest,
however, may not adequately reflect the true cost in borrowing. To
compare different loan schemes on the same basis we propose to
use the equivalent nominal rate of interest, which is appropriate for
comparing loans with the same frequency of repayment installments.