1. [25p] An amortized loan of $75,000 has annual payments for eighteen years, the first occurring exactly one year after the loan is made. The first four payments will be for only half as much as the remaining fourteen. The annual effective interest rate for the loan is 6%. Calculate the amount of principal repaid in the seventh payment.

2. [20p] Helen borrows $20000 to be repaid over 15 years with level annual payments with an annual effective interest rate of 8%. The first payment is due one year after she takes out the loan. Helen pays an additional $4000 at the end of year 9 (in addition to her normal payment). At that time (the end of year 9) she negotiates to pay off the remaining principal at the end of year 14 with a sinking fund. The sinking fund accumulates at an annual effective interest rate of 7%. Helen will make level annual payments and she will also make annual interest payments at an annual effective interest rate of 10%. You may assume all payments are made at the end of the year. Determine Helen's total annual outlay starting with year 10.

3. [25p] A $1,000 6% n-year par-value bond has annual coupons. Tabitha bought the bond to yield 5%. The amount of interest in the first coupon is $52.89. Calculate the amount of premium Tabitha paid for the bond.

4. [15p] A $1,000 8% 20-year bond with semi-annual coupons is purchased for $1014. The redemption value is $1000. The coupons are reinvested at a nominal annual rate of 6%, compounded semi-annually. Determine the purchaser's annual effective yield rate over the 20 year period.

5. [15p] An investor bought a 15-year bond with par value of 100000 and 8% semi-annual coupons. The bond is callable at par on any coupon date beginning with the 24th coupon. Find the highest price paid that will yield a rate not less than i (2) = 10%.