Questions: Hans wants to buy a bond that will mature to 5500 in seven years. How much should he pay for the bond now if it earns interest at a rate of 2% per year, compounded continuously? Do not round any intermediate computations, and round your answer to the nearest cent.

Solution Steps

To convert the annual interest rate \(r = 2\%\) to a decimal, we divide by 100: \(r = 0.02\).

The discount factor is calculated using the formula \(e^{-rt}\), where \(e\) is the base of the natural logarithm, \(r\) is the annual interest rate as a decimal, and \(t\) is the time in years. Thus, the discount factor is \(e^{-0.02 \times 7} = 0.869\).

The present value \(P\) is found by multiplying the future value \(A = 5500\) by the discount factor: \(P = A \times e^{-rt} = 5500 \times 0.869 = 4781.47\).

Final Answer: The present value of the bond is 4781.47.