Final answer:
The present value of $2000 due in 3 years with continuous compounding at a 4% interest rate is calculated using the formula PV = FV * e^(-rt), resulting in a present value of $1773.80.
Step-by-step explanation:
Calculating Present Value with Continuous Compounding
The question involves determining the present value of a future sum of money with continuously compounded interest. In this case, the future sum is $2000, the interest rate is 4%, and the time period is 3 years. The formula for continuous compounding is given by PV = FV * e^(-rt), where PV is the present value, FV is the future value, r is the interest rate, and t is the time in years.
Plugging the given values into the formula:
r = 4% or 0.04
t = 3 years
We calculate the present value (PV) as follows:
PV = 2000 * e^(-0.04 * 3)
PV = 2000 * e^(-0.12)
PV = 2000 * 0.8869 (using a calculator)
PV = $1773.80 (rounded to the nearest cent)
Therefore, the present value of $2000 payable at the end of 3 years with continuous compounding at a 4% interest rate is $1773.80.