# Fixed-Income Q

Three years ago, at the advice of her financial planner, an investor purchased a \$1K face, 4.5%, S-Annual coupon Bond with 7Y to maturity priced to yield 6.5% for \$888.94. The reinvestment income that must be generated over the life of the bond for the investor to realize a yield of 6.5% is … ?

~ \$76?

how?

Semiannual compound rate is 0.065/2 = 0.0325 Ending value must be \$888.94(1.0325)14 = \$1,391.02. \$1,391.02 –1,000.00 face value at maturity ----------- 391.02 –315.00 total coupons (14 × 22.50) ----------- 76.02

\$66. Total income from the bond = 888.94 * (1.065)^7 = 1381.4 Total income = maturity value + coupon pmts + reinvestment income 1381.4 = 1k + (4.5%/2 * (7 * 2) * 1K) + x x = 1381.4 - 1k - 315 = \$66

I like Cavil’s better because the 6.5% ytm is based on the semi-annual compounding, not the annual compunding done by HJAA

with cavil that was in vol 6. 1 am exam

Fair - with the TVM set to semi-annual compounding (i.e. n = 14), i/y = 3.25. => 888.94 * (1.0325^14) = 1391.0 So is YTM always quoted as an uncompounded annualised figure (e.g. 2 * semiannual YTM)? I always thought it was just the annual IRR of the CF.

Just checked - my mistake. YTM = I/Y * # periods / year.