Reinvestment Income par, following, payments, security, correct

toocfatoo

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???

lc26mizzou

1 + 0.07515/2

RobertA

Where are you getting the 1.0376 from?

Daniel1985

I agree with 340.

homie

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

JRossSter

Nevermind I am being an idiot.

marsilni

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