# Reinvestment Income

XYZ purchases a 4-year, 6%, semiannual-pay Treasury note for \$9,485. The security has a par value of \$10,000. To realize a total dollar return equal to 7.515% (its yield to maturity), XYZ must have which of the following reinvestment assumptions? A) All payments must be reinvested at more than 7.515%. B) All payments must be reinvested at 7.515%. C) All payments must be reinvested at less than 7.515%. Without doing the math the obvious ans is B (which is also the correct ans). However, if I do the math… something doesn’t match up Total dollar return = 9485*(1.03)^8 - 9845 = 2530.31 Coupon payment + Gain on sec + Reinvestment Income = 2530.31 2400 + (10000-9485) + Reinvestment Income = 2530.31 Reinvestment Income = -385… Is the solution wrong or am I wrong???

I believe the answer is C. The return will fall somewhere between the coupon rate and the ytm.

Nevermind I am being an idiot.

To find the required dollar return you’re supposed to use purchase price and required compound rate: 9485 * (1.0376)^8 = 12,740.7 Take away principal and coupon payments (10,000 + (300 * 8) = 12,400) to get RI Reinvestment Income = 12,740 - 12,400 = 340

I agree with 340.

Where are you getting the 1.0376 from?

1 + 0.07515/2