How much must be invested today at 10 %, compounded continuously, to be worth $165,000 in 5 years? Pick the closest answer. [Use e = 2.71]

To solve this problem, we will use the formula for continuous compounding, which is:

A = P * e^(rt)

Where: A = the amount of money accumulated after n years, including interest. P = the principal amount (the initial amount of money) r = annual interest rate (decimal) t = time the money is invested for in years

We know that A = $165,000, r = 10% or 0.10, t = 5 years, and we need to find P.

Rearranging the formula to solve for P gives us:

P = A / e^(rt)

Substituting the given values into the formula gives us:

P = 165000 / 2.71^(0.10*5)

Now, calculate the value of P.

P = 165000 / 2.71^(0.5)

P = 165000 / 1.6487212707

P = $100,000.17

So, approximately $100,000 must be invested today at 10$165,000 in 5 years.