FM for Actuaries

Loans and Costs of Borrowing 181
5.46 Construct a sinking fund schedule for a loan of $2,500 to be repaid over 5
years at 7%. It is assumed that the sinking fund earns 7% per year.
5.47 Construct a sinking fund schedule for a loan of $2,500 to be repaid over 5
years at 7%. It is assumed that the sinking fund earns 6% per year. Compare
your results with that in Exercise 5.46.
5.48 Construct a sinking fund schedule for a loan of $2,500 to be repaid over 5
years at 7%. It is assumed that the sinking fund earns 6% per year, while the
interest in the sinking fund can only be reinvested at 5% effective. Compare
the results with those in Exercise 5.46 and Exercise 5.47.
5.49 Gary took out a loan of $2,300 at an annual effective rate of 6%. Level
interest payments are made at the end of every year for 8 years, and the
principal is repaid at the end of 8 years by the accumulation of a sinking
fund earning 5% effective. Find the difference between the interest payment
earned by the sinking fund and the interest payment on the loan.
5.50 Paul borrows $53,000 and repays the principal by making 10 payments at
the end of each year into a sinking fund earning an effective rate of 7.5% per
annum. The interest earned on the sinking fund in the kth year is $2,035.40.
Find k.
5.51 Jennifer took out a $6,000 loan from a bank and agreed to make interest
payments every 6 months at a nominal rate of 6% compounded semiannually.
At the end of 3 years she would repay the principal. In the meantime, Jennifer
made deposits into a sinking fund earning an annual effective rate of 4.04%.
(a) Find the total payment made by Jennifer every 6 months.
(b) Find the sinking fund balance after 2 years.
(c) Find the net interest served to the loan in the 5th payment to the lender.
5.52 A loan of $3,000 at effective rate of interest of 4% per year is to be redeemed
over 10 years by a sinking fund that credits interest at 3.5%. When the 5th
payment is due, the borrower can only pay the interest payment to the lender
but is not able to make the sinking fund deposit. In order to repay the loan
on time, the borrower pays an extra K dollars in the 6th to 10th sinking fund
deposits. Find K.
5.53 Eddy borrowed $10,000 from a bank for 15 years at an annual effective rate
of 6%. He paid interest annually and also made annual level deposits in a
sinking fund which would repay the debt at the end of 15 years. The sinking
fund earns 5% in the first 8 years and then 6% in subsequent years.