Question

2. Kate bought a bond at face value of $1000 at inception in the market. The life of the bond is 20 yeats, coupons are paid yearly with bond rate of 5%. She holds it for 8 years and sells it at a price that yields is 4% on her investment. What would the yield for the second owner be if the second owner holds it until maturity? l anded

Answer 1

Coupon payment = 5% * 1000 = 50

Let sale price of bond be S, then

1000 = 50 * (P/A,4%,8) + S *(P/F,4%,8)

1000 = 50 * 6.732745 + S *0.730690

S = (1000 - 50 * 6.732745) / 0.730690

S = 907.86

Let yeild be i%, then

907.86 = 50 * (P/A,i%,12) + 1000 * (P/F,i%,12)

using trail and error method

When i = 6%, then 50 * (P/A,i%,12) + 1000 * (P/F,i%,12) = 50 * 8.383844 + 1000 * 0.496969 = 916.16

When i = 7%, then 50 * (P/A,i%,12) + 1000 * (P/F,i%,12) = 50 * 7.942686 + 1000 * 0.444012 = 841.14

using interpolation

i = 6% + (916.16 - 907.86) / (916.16 - 841.14)*(7%-6%)

i = 6% + 0.11%

i = 6.11%