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Find the present value of $2000 payable at the end of 3 years, if money may be invested at 4% with interest compounded continuously. The present value of $2000 is $ (Round to the nearest cent as needed.)

User Nabnub
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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.

User Nigel Touch
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