Question

How do you do this problem? I don't understand how they got the answer.

Wally purchases a bond on Jan 1, 2015 with a face value of $25,000 that matures in 3 years. The coupon rate for the first payment is 3% on Jan 1, 2016, for the second payment is 4% on Jan 1, 2017, the last payment is 5% on Jan 1, 2018. On Jan 1, 2016, Wally decides, after he receives the coupon payment, that he wants to sell his bond to Samantha. If the market interest rate is 2% what price will Wally sell his bond for.?

The answer is apparently $26,211.

Answer 1

Market rate = 2%

Face value = 25000,, Maturity = 3 years

Coupon rate for first year = 3%, Coupon payment for first year = 0.03 * 25000 = 750

Coupon rate for second year = 4%, Coupon payment for second year = 0.04 * 25000 = 1000

Coupon rate for third year = 5%, Coupon payment for third year = 0.05 * 25000 = 1250

After receiveing first payment, bond is to be sold, so we need to find value of bond by discounting its future payments at market rate

We use formula P = F/(1+i)^t to discount future cash flows

Value of bond after 1 year = 1000/1.02 + 1250/1.02² + 25000/1.02²

= 980.392 + 1201.4609 + 24029.219

= 26211.072

= 26211 (rounding off)