Question

Ann wants to buy a bond that will mature to $4500 in seven years. How much should she pay for the bond now if it earns interest at a rate of 3% per year, compounded continuously?

Do not round any intermediate computations, and round your answer to the nearest cent.

Answer 1

Ann should pay approximately $3,643.97 for the bond now to achieve the maturity value of $4,500 in seven years with continuous compounding at a 3% interest rate.

Step-by-step explanation:

The question asks us to calculate the present value of a bond that will mature to $4,500 in seven years with an interest rate of 3% per year, compounded continuously.

To find the present value (PV), we use the formula for continuous compounding: PV = P*e^(-rt), where P is the maturity value, r is the interest rate, and t is the time (in years).

Let's calculate it:

• P = $4,500 (maturity value)
• r = 3% or 0.03 (interest rate)
• t = 7 years (time to maturity)

Using the formula:
PV = $4,500 * e^(-0.03*7)
PV = $4,500 * e^(-0.21)
PV = $4,500 * 0.809782[using a scientific calculator for e^(-0.21)]
PV = $3,643.97

Therefore, Ann should pay approximately $3,643.97 for the bond now if it earns interest at a rate of 3% per year, compounded continuously.