Find the present value of $\$ 5000$ payable at the end of 2 years, if money may be invested at $7 \%$ with interest compounded continuously.
Answer
So, the present value of $5000 payable at the end of 2 years, if money may be invested at 7% with interest compounded continuously, is approximately \(\boxed{4346.79}\).
Step 1 ：Given that the future value (FV) is $5000, the interest rate (r) is 7% or 0.07, and the time (t) is 2 years.
Step 2 ：The formula for the present value (PV) when interest is compounded continuously is given by: \(PV = FV * e^{-rt}\), where e is the base of the natural logarithm, approximately equal to 2.71828.
Step 3 ：Substitute the given values into the formula: \(PV = 5000 * e^{-0.07*2}\).
Step 4 ：Calculate the present value to get approximately $4346.79.
Step 5 ：So, the present value of $5000 payable at the end of 2 years, if money may be invested at 7% with interest compounded continuously, is approximately \(\boxed{4346.79}\).
