Janet Woo decided to retire to Florida in 5 years. What amount should Janet invest today so she can withdraw $45,000 at the end of each year for 20 years after she retires? Assume Janet can invest money at 5% compounded annually.

To calculate the amount that Janet needs to invest today in order to withdraw $45,000 at the end of each year for 20 years after she retires, we can use the concept of Present Value (PV) and the formula for calculating the present value of an ordinary annuity.

The formula for the present value of an ordinary annuity is:

PV = P * [(1 - (1 + r)^-n) / r]

Where:
PV = Present Value (the amount Janet needs to invest today)
P = Payment per period ($45,000)
r = Interest rate per period (5% or 0.05, compounded annually)
n = Number of periods (20 years)

Let's plug in the values into the formula:

PV = $45,000 * [(1 - (1 + 0.05)^-20) / 0.05]

Now, we can solve the equation to find the present value (PV).

PV = $45,000 * [1 - (1.05)^-20] / 0.05

Calculating this formula will give us the amount Janet needs to invest today in order to withdraw $45,000 annually for 20 years after she retires.

janet won lottery an receives $10 the 1st year. in the following years, she receives $50 more each year, (that is, janet receives $150 the second year, $200 the third, and so on) How much will she receive in total after 10 years