UECM1403 Theory of Interest (Jan 2015) Assignment (10%)

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Section A: Solve the following problems, show all working steps.

1. An investor buys two 20-year bonds, each having semi-annual coupons and each maturing at par value. For

each bond, the purchase price produces the same yield rate. One bond has a par value of RM500 and a

coupon of RM45. The other bond has a par value of RM1000 and a coupon of RM30. The dollar amount of

premium on the first bond is twice as great as the dollar amount of discount on the second bond. Find the

yield rate convertible semi-annually.

2. A one-year RM100 Treasury bond with 10% semi-annual coupon sells for RM102.875. A one-year RM100

Treasury bill sells for RM93.35. Determine the forward rate applicable to the six-month period starting six

months from now, expressed as a nominal annual rate convertible semi-annually.

3. A perpetuity-immediate has annual payments of 1.05, 1.052, 1.05

3,..... Determine the duration of this

perpetuity at an effective interest rate of 10%.

Section B: IN YOUR OWN WORDS, explain the following scenarios in detail.

1. Consider a loan being repaid using the sinking fund method, where interest paid to lender is constant each

period at the rate i but the sinking fund deposits vary. The varying total payments by borrowers are

1 2, , , nR R R while the sinking fund deposit for the t th period is tR iL , the sinking fund earns at the rate

j, i j . The original loan amount is given as

Without proving the formula, explain the meaning of this formula with the help of time diagram. I.e.,

explain the rationale of every component in the summation 1

1n n t

ttR j

and also in the subtraction on

the right side at the rate j.

2. Consider a callable bond where the borrower has an option to redeem prior to the normal maturity date.

When determining the bond price, explain the reason of choosing

a) earliest redemption date if the bond sells at a premium and latest redemption date if the bond sells at a

discount

b) the lowest price when there are different call prices at different call periods (from the point of view of

bond buyers)

3. Consider the investments of 1 at the end of each period for n periods at the rate i such that the interest is

reinvested at rate j. Draw the time diagram and derive the formula for the accumulated values of the above

investment, explain in words the accumulation process along the time diagram.