The U. S. Treasury issued a 20-year bond on November 16, 1998, paying 6.07% interest. Thus, if you bought $100,000 worth of these bonds, you would receive $6,070 per year in interest for 20 years. At investor wishes to buy the rights to receive the interest on $100,000 worth of these bonds. The amount the investor is willing to pay is the present value of the interest payments, assuming a 6% rate of return. If we assume (incorrectly, but approximately) that the interest payments are made continuously, what will the investor pay Round your answer to the nearest cent.
A)$70,695.85
B) $437,051.83
C) $335,885.16
D) $69,880.58
E) $706.96

Question

The U. S. Treasury issued a 20-year bond on November 16, 1998, paying 6.07% interest. Thus, if you bought $100,000 worth of these bonds, you would receive $6,070 per year in interest for 20 years. At investor wishes to buy the rights to receive the interest on $100,000 worth of these bonds. The amount the investor is willing to pay is the present value of the interest payments, assuming a 6% rate of return. If we assume (incorrectly, but approximately) that the interest payments are made continuously, what will the investor pay  Round your answer to the nearest cent.  
A)$70,695.85
B) $437,051.83
C) $335,885.16
D) $69,880.58
E) $706.96

Quizplus · Accepted Answer

The present value of continuous interest payments can be calculated using the formula for the present value of a continuous annuity: PV = C * (1 - e^(-rt)) / r, where C is the annual interest payment, r is the rate of return, and t is the time period. Plugging in the values: PV = 6070 * (1 - e^(-0.06*20)) / 0.06, which results in approximately $70,695.85.

The U S Treasury Issued a 20-Year Bond on November 16, 1998