Question

Question 1 (14 marks) (a) Eric is scheduled to receive $8000 in two years. When he receives it, he will invest it for five years at 6 percent per year. How much will he have in seven years? (3 marks) (b) Suppose you are going to receive $12,000 per year for five years. The appropriate annual interest rate is 8 percent. What is the present value of the payments if they are in the form of an ordinary annuity? Will the present value be higher or lower if it was an annuity due? Show your calculation. (5 marks) (c) Consider a semiannual coupon bond with a 8% coupon rate. The par value is $1000. If the bond is priced to yield 6% YTM, and it has 10 years to maturity. Do you think it is a discount bond or premium bond? Please show the bond price to justify your answer. (6 marks)

Answer 1

a) Amount received after 2 years = $8.000 investment rate = 6% p.a. Amount after 7 years = Px (1+4)" P = amane inwesked ri rate of return n = number of years as we are investing after two years so our 'ñ would be '7-2=5 = 8000 X (1+0.06 80000 (1.0605 = 8000 x 1033823 Amount after 7 years =$10,705.84 Amount after 7 years

8% p.a. ano + b) Annuity Paymats (P) = $12,000 per year for sycaus Interest rate (r) IP.V. of ordinary annuity = f 오 오 eth (tr) (Itaga (ltr)? (14884 (Hejs 12.000 4 12.000 + 12000 12000 (1+0.08) (HooB} (1+0.08)3 (1+0.09 (1+0.08 = 11:11 + 10,288.066 +9525.987 +8820.358 + 8,166.99 - $ 47,912.52 P. U. of annuity due = pt f P + P CHA) (ltr)² (+2)3 = 12,000+ 12.000 1 2009 +12.000 CH0.08) C1+0.089 (+0.08)(+0.08) = 12000 + 11,11. 10,288.0 60+9,525.987+882358 =$51745.52 02 (tr) + 1200 o. P. U. of annuity due > P. v. of ordinary annuity

c) Coupon Rate = 8% par value = $i poo YTM - 6%. Time : 10 years Whenever YTM < Coupon hate it means bond is priced at premium and vice versa Calculation of brice : brice present Value of future Coupons + present value of Maturity value