Financial Mathematics Test Questions for 2013 Fall Semester

1.        Given a nominal interest rate of 7.5% convertible semiannually, determine the sum of the equivalent:

            i.              Force of interest; and

          ii.              Nominal discount rate compounded quarterly.

2.        Susan and Jeff make deposits of 100 at the end of each year for 40 years.

 Starting at the end of the 41^st years, Susan makes annual withdraws of X for 15 years and Jeff makes annual withdraws of Y for 15 years. Both funds have a balance of 0 after the last withdrawal.

Susan’s fund earns an annual effective interest rate of 8%.Jeff’s fund earns an annual effective interest rate of 10%.Calculate  Y-X.

3.     1000 is deposited into a fund on Jan1,1992. Another deposit is made into the fund on July1,1992. On Jan1,1993,the balance in the fund is 2000. The time-weighted yield rate is 10% and the dollar-weighted yield rate is 9%.Calculate the annual effective interest rate earned on the fund during the first six months of 1992.

4.        A  10-year loan of 10,000 is to be repaid with payments at the end of each year consisting of interest on the loan and a sinking fund deposit. Interest on the loan is charged at a 12% annual effective rate. The sinking fund’s annual effective interest rate is 8%. However, beginning in the sixth year, the sinking fund’s annual effective interest rate on the sinking fund drops to 6%.As a result, the annual payment to the sinking fund is then increase by X. Calculate X.

5.        Bill buys a 10-year 1000 par  value 6% bond with semiannual coupons. The price assums a nominal yield of 6%, compounded semiannually. As Bill receives each coupon payments, he immediately puts the money into an account earning interest at an annual effective rate of  i. At the end of 10 years, immediately after Bill receives the final coupon payment and the redemption value(偿还价值) of the bond, Bill has earned an annual effective yield of 7% on his investment in the bond. Calculate i.

6.        A stock has a current price of $65. A dividend of $3.25 is expected of be paid in 6 months. The risk-free interest rate is 10% effective per annual. X is the forward price of a one-year forward contract that has the stock as the underlying asset. Determine X.

7.        The call premium for a non-dividend-paying stock exceeds the put premium by $19.608, where both options have a strike price of K. The put premium on the same stock exceeds the call premium by $29.412, where both options have a strike price that is 5%greater than K. The effective rate of  interest for the period from time 0 to the expiration date of the options is 2%.Determine K and the current stock price.

8.        You are given the following spot rates:

It is known that one-year forward rate for year 4 is 5.34%. Determine X.

Solution

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