The Megabucks Corporation is issuing a 5-year bond paying 8% interest. An investor wishes to buy the rights to receive the interest on $90,000 worth of these bonds and seeks a 6% rate of return. If the investor payments are made continuously, what will the investor pay?
A)$281,983.06
B)$31,101.81
C)$311.02
D)$120,000.00
E)$1,866.11

Question

Quizplus · Accepted Answer

First, we need to find the present value of the bond investment. Using the formula for present value of a bond:
PV = FV/(1+r)^n
where PV is the present value, FV is the future value (in this case, the amount of the bond investment), r is the interest rate, and n is the number of years.
Plugging in the values:
PV = $90,000/(1+0.08)^5 = $59,676.77
Now, we can use the formula for the present value of an annuity:
PV = (PMT/r)(1-1/(1+r)^n)
where PMT is the periodic payment, r is the interest rate, and n is the number of periods.
We want to solve for PMT, so we can rearrange the formula:
PMT = PV*r/(1-1/(1+r)^n)
Plugging in the values:
PMT = $59,676.77*0.06/(1-1/(1+0.06)^(5*365)) = $31,101.81
Therefore, the investor will pay $31,101.81 for the rights to receive the interest payments on $90,000 worth of bonds. So the best choice is B.

The Megabucks Corporation Is Issuing a 5-Year Bond Paying 8