FM for Actuaries

176 CHAPTER 5
5.23 A loan of amount L is to be repaid with level installments P at the end of
each year for as long as necessary, plus a smaller final payment. The interest
rate charged by the lender is i per year. Assume that P>iLso that there is
no negative amortization. Construct an amortization schedule by following
the steps below.
(a) Calculate the outstanding loan balance. [Hint: Prospective method
does not work.]
(b) Calculate the interest paid in each period.
(c) Calculate the principal repaid in each period.
(d) Determine n, the number of payments needed, and the size of the final
irregular payment. How is this final payment split into interest and
principal repaid?
Show that the principal repaid (except the one corresponding to the final
installment) is an increasing geometric sequence. This observation is useful
in the construction of the amortization schedule. Note that if the installments
are level, then the principal repaid forms a geometric sequence in view of
Table 5.1.
5.24 Construct an amortization schedule for the loan in Exercise 5.7.
5.25 A loan of $10,000 is to be repaid with level installments of $1,800 per month
for as long as necessary, plus a smaller final payment. The nominal rate of
interest convertible monthly is 12%. Construct an amortization schedule for
the loan.
5.26 A loan is being repaid with level installments except for the final smaller
adjustment payment. Complete the following amortization schedule:
Year Installment Interest paid Principal repaid Outstanding balance
0
1 970.00
2
3 1,131.41
4 351.00 0
5.27 A loan is being repaid with level installments except for the final smaller
adjustment payment. Complete the following amortization schedule: