20.Assume that you just graduate and get a job. You will work for 40 years and save each year before you retire. During retirement you plan to receive a pension annuity of $100,000 each year for another 40 years. How much money will you need to have at the moment you retire? How much money do you need to save every year before retirement? Assume the interest rate is always 8%. Before retirement, you deposit your saving at the end of each year. During retirement, you receive the annuity at the beginning of each year

How much money will you need to have at the moment you retire?

How much money do you need to save every year before retirement?

Explanation:

we have to first determine the amount of money you need to finance your retirement distributions:

using the annuity due present value formula, PV = annuity payment x annuity due factor (PV, 8%, n = 40)

PV = $100,000 x 12.87858 = $1,287,858

now we must use the ordinary annuity future value formula, FV = annuity payment x annuity factor (FV, 8%, n = 40)

annuity payment = FV / annuity factor = $1,287,858 / 259.057 = $4,971.33

a manufacturer of printed circuit boards uses exponential smoothing with trend to forecast monthly demand of its product. at the end of december, the company wishes to forecast sales for january. the estimate of trend through november has been 200 additional boards sold per month. average sales have been around 1000 units per month. the demand for december was 1100 units. the company uses α = 0.20 and β = 0.10. make a forecast including trend for the month of january.