### DEPARTMENT OF MATHEMATICS & STATISTICS MATH 3803

 FINAL EXAMINATION DECEMBER 1996 TIME: 3 HOURS

Answer all questions. Credit will be given for presentation and methods of solutions.

 1. Given where t is measured in years with , find (a) the effective rate of discount over the 4th year; (b) the force of interest; (c) the amount of interest earned in the 7th year; (d) the equivalent annual rate of interest for the 10 year period. 2. Find the present value of \$5000 due in 20 years under the following rates: (a) ; (b) ; (c) ; (d) a simple rate of discount of 4%. 3. Find the accumulated value of \$2000 over 10 years under the following rates: (a) ; (b) ; (c) ; (d) . 4. An annuity-immediate has a term of 30 years, and an annual rate of interest of 9%. Calculate the present and accumulated values of the annuity for the following sets of payments: (a) \$1000 in each of the first 15 years, and \$2000 in each year thereafter; (b) \$1000 in each of the first 10 years, \$1500 in each of the second 10 years and \$500 in each year thereafter.
 5. (a) Calculate the following numbers under a rate of interest of 10%: (i) ;(ii) ;(iii) ;(iv) . (b) An annuity has payments of \$200 every 3 months for 4 years. Calculate the present value of this annuity under the following conditions: (i) and the payments are made at the start of each 3-month period; (ii) and the payments are made at the end of each 3-month period.
 6. (a) Calculate how long \$1000 should be left to accumulate at 6% effective in order that it may amount to twice the accumulated value of another \$1000 deposited for the same time at 4% effective. (b) Payments of \$100.00 made at the end of every month accumulate to \$3000 at the end of two years. Use interpolation of the tables to find the effective rate of interest per month; and deduce the effective rate of interest per year. 7. A loan of \$10,000 is to be repaid by payments of \$1000 at the end of every year for as long as necessary with an extra payment being made one year after the last \$1000 payment. If the rate of interest charged to the loan is 5%, determine the amount of this extra payment. 8. (a) A loan of \$100,000 at 9% convertible half-yearly is repaid by the amortization method with level payments at the end of every half-year for 25 years. Calculate the amount of interest in the 30th payment. (b) A loan of \$100,000 is being repaid by the sinking fund method with annual payments at the end of every year for 20 years. If the rates of interest charged to the loan, and earned by the sinking fund, are both 8%, calculate the amount in the sinking fund after the twelfth payment.