Find the present value of $\$ 5000$ payable at the end of 2 years, if money may be invested at $3 \%$ with interest compounded continuously.
The present value of $\$ 5000$ is $\$$ (Rognd to the nearest cent as needed.)
Answer
Rounding to the nearest cent, the present value of $5000 payable at the end of 2 years, if money may be invested at 3% with interest compounded continuously is approximately \(\boxed{\$4708.82}\)
Step 1 ：We are given that the future value (FV) is $5000, the interest rate (r) is 3% or 0.03, and the time (t) is 2 years. We are asked to find the present value (PV).
Step 2 ：We can use the formula for continuous compounding to find the present value: \(PV = FV * e^{-rt}\), where e is the base of the natural logarithm, approximately equal to 2.71828.
Step 3 ：Substituting the given values into the formula, we get: \(PV = 5000 * e^{-0.03*2}\)
Step 4 ：Solving the above expression, we find that the present value (PV) is approximately 4708.822667921244
Step 5 ：Rounding to the nearest cent, the present value of $5000 payable at the end of 2 years, if money may be invested at 3% with interest compounded continuously is approximately \(\boxed{\$4708.82}\)
