Question

Write out the formulas, with the numbers filled in, to solve the following problems. You do not have to do the actual calculations. Find the yield-to-maturity of a zero-coupon 10-year bond (par = $1,000) with a price of $622.44. (4 points). Find the present value of an investment that has three payments: $400 in two years, $500 in four years and $600 eight years from today. The relevant market interest rate is 4.20%. Find the future value of $100 invested today for 5 years at an annual rate of 6%, paid monthly.

Answer 1

Q1

value of zero coupon bond = face value / ( 1 + yield to maturity )^ no of years to maturity

622.44= 1000 / (1 +ytm)^10

( 1+ytm)^10 = 1000 /622.44

1+ ytm = 1.0486

ytm = 4.86%

Q2.

Present value of investment = cashflow in 2 years / ( 1+int rate )^2 + cashflow in year 4 / ( 1 + int rate )^4 + cashflow in year 8 / ( 1 + intrate )^8

= 400/1.042^2 + 500/1.042^4 + 600/1.042^8

= 1224.26

Q3.

Future value = present value * ( 1 + periodic yield)^ no of periods

= 100*1.005^60

= 134.89