FM for Actuaries

Loans and Costs of Borrowing 177
Year Installment Interest paid Principal repaid Outstanding balance
0
1 1,550
2 138 1,838
3
4 0
5.28 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
1 200.00
2 150.00
3 97.50
4 0
5.29 A loan is to be repaid with $1,000, $2,000, and $3,000 at the end of the
1st, 2nd and 3rd year. Interest is payable semiannually at a nominal rate of
5%. Construct an amortization schedule for the loan. Interests payable in the
middle of the year are debited into the loan balance.
5.30 A loan is originally scheduled to be repaid with 9 annual level payments of
$500 at rate i. When the 6th payment is due, the borrower only pays the
interest due. At the end of the 7th year, the borrower cannot even pay the
interest then due, but finally pays off the loan by level installments of P at
the end of the 8th, 9th, 10th and 11th year. Assuming that the lender does not
charge a higher interest to penalize the borrower for delaying the payment,
by how much is P greater than $500?
5.31 A loan of $1,000 is to be repaid with annual payments of $50, $100, $1,000
and P at the end of the 1st, 2nd, 3rd and 4th year. The interest rate is 10%
per annum. Construct an amortization schedule for the loan and determine
P .
5.32 Richard purchases a car for $30,000, paying down $7,000, and $800 at the
end of each month until the debt is redeemed. If the interest rate charged on
the loan is 6% convertible monthly, how long will it take to redeem the loan?
What is the size of the final irregular payment?