Your brother would like to have $27,000 in 3 years for the purchase of a new car. What monthly payment should he make into an account paying 7% per year compounded monthly to attain his goal?

The monthly payment which is required to achieve the goal is $676.18

Explanation:

The  monthly payment which is required to achieve the goal is computed as:

Using the excel formula of PMT:

=PMT(rate,nper,pv,fv,type)

where

PMT is payment monthly

rate is 7%

but rate is compounded monthly, so

r = 7%/ 12

nper is number of years which is 3 years

but the number of years also compounded monthly, so

nper = 3 × 12

fv is future value, which is $27,000

Putting the values above:

=PMT(7%/12,3 × 12,0,-27000,0)

= $676.18

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.