What is the future worth of $1,000 in month 1, $1,040 in month 2, and amounts increasing by $40 per month through month 12, at the end of year 2 if the interest rate is 23.7631528% per year, compounded continuously?

To calculate the future worth of the given cash flows, we can use the formula for continuous compounding:

A = P * e^(rt)

where:
A = future worth
P = present value (initial investment)
e = Euler's number (approximately 2.71828)
r = interest rate per period
t = number of periods

First, let's calculate the monthly interest rate by dividing the annual interest rate by 12:

r = 23.7631528% / 12
r = 0.0237631528

Next, we can substitute the values into the formula for each cash flow and sum them up to find the future worth:

A = $1,000 * e^(0.0237631528 * 1) + $1,040 * e^(0.0237631528 * 2) + ($1,040 + $40) * e^(0.0237631528 * 3) + ... + ($1,040 + $40 * 10) * e^(0.0237631528 * 12)

Note that we start from $1,040 in the second month and increase by $40 each subsequent month until the 12th month.

To solve this equation, we need to use a calculator or a programming environment that can handle exponential calculations with Euler's number.