Suppose a worker retires with a savings of $500,000 which is in an interest bearing account that has a rate of 6% per year. If after retirement the worker spends $4,000 a month, will there be any money left after 10 years

Yes there will be money left in the account after 10 years.

Explanation:

The original amount at the start of retirement = $500,000

annual interest rate = 6% = 0.06

First of all, $4,000 is spent monthly for the next 10 years, let us calculate the total amount spent:

10 years of 12 months per year = 10 × 12 = 120 months

if $4,000 is spent per month, then total amount spent after 10 years (120 months) = 120 × 4000 = $480,000. This amount is less than the original saved amount of $500,000, hence, in the absence of any interest, the invested amount is higher than the amount spent by $20,000, suggesting that there will be some money left in the account after 10 years.

Next let us calculate the total amount on the sum if simple interest is applied on the original amount.

Simple interest = Principal × rate × time

Therefore simple interest on the sum for a period of 10 years =

500,000 × 0.06 × 10 = $300,000

hence the total return after 10 years =

500,000 + 300,000 = $800,000

Next, if $4,000 is spent monthly for the next 10 years, $480,000 will be spent in total (calculated above)

Therefore, amount left in the account = 800,000 - 480,000 = $320,000

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.