Question

Evaluate which of the following options would be your best investment based solely on the yield to maturity criterion.

    Option #1: Purchase a $20,000 discount bond selling for $16,200 and maturing in 6 years.       

    Option #2:  Purchase a $20,000 coupon bond with a 5.5% coupon rate selling for $10,600 and maturing in 6 years.

    Option #3: Lend a reliable friend $15,000 with the agreement that she pays you $6,534.80 five years from now,

                       $8,540.72 ten years from now, and $11,162.38 fifteen years from now. (Note: each future payment

                       represents an equal present value amount).

Answer 1

1) OPTION 1:

Future value = $20,000

Present value = $16,200

n = 6 years

fv = pv(f/p,i,n)

20,000 = 16,200(f/p,i,6)

20,000 / 16,200 = (f/p,i,6)

1.2345 = (f/p,i,6)

solving for i via trial and error we get i = 3.57442% (by solving for various values of i)

2) Option 2:

Future value = $20,000

pv = $10,600

coupon rate = 5.5%

n = 6 years

coupon payment = coupon rate * future value = 5.5% * 20,000 = 1,100

future value = present value(f/p,i,n) + coupon payment(f/a,i,n)

20,000 = 10,600(f/p,i,6) + 1,100(f/a,i,6)

solving for i via trial and error we get i = 19.43568% ( by solving for various values of i)

3) Option 3:

Present value = $15,000

payment recieved in 5 years = $6,534.8

payment recieved in 10 years = $8,540.72

payment recieved in 15 years = $11,162.38

present value = payment recieved in 5 years(p/f,i,n) + payment recieved in 10 years(p/f,i,n) + payment recieved in 15 years(p/f,i,n)

15,000 = 6,534.8(p/f,i,5) + 8,540.72(p/f,i,10) + 11,162.38(p/f,i,15)

solving for i via trial and error we get i = 5.49999% ( by solving for various values of i)

Based on the yield , option 2 is the best as it has the highest yield of 19.43568%