A manufacturer of prototyping equipment wants to have $3,000,000 available 10 years from now so that a new product line can be initiated. If the company plans to deposit money each year, starting one year from now, the equation that represents how much the company is required to deposit each year at 10% per year interest to have the $3,000,000 immediately after the last deposit is

annual savings = future value / [(1 + r)ⁿ - 1 ] / n

annual savings = $3,000,000 / [(1 + 0.1)¹⁰ - 1 ] / 0.1

annual deposit = $188,236.18

Explanation:

this is an ordinary annuity

future value = $3,000,000

interest rate = 10%

periods = 10

using the future value of an annuity formula, annual deposit = future value / annuity factor

FV annuity factor, 10 periods, 10% = 15.937

annual deposit = $3,000,000 / 15.937 = $188,241.20

instead of using annuity factors, you can solve this equation:

annual deposit = future value / [(1 + r)ⁿ - 1 ] / n

annual deposit = $3,000,000 / [(1 + 0.1)¹⁰ - 1 ] / 0.1

annual deposit = $188,236.18

Both answers are very similar, the difference is only 0.00267%

answer: in the short-run firms will respond by raising the price of turkey.

explanation: initially the long-run equilibrium is at a price of $5 per pound of turkey and a quantity of 50 million pounds per year. now, when webmd claims that a protein found in turkey will increase your expected lifespan by 4 years. the consumers demand for turkey will increase at every price shifting the demand curve to the right from d1 to d2. while, there will be no change in the supply curve in the short-run as it is not possible for producers to adjust supply so quickly. as a result the new equilibrium will occur at a higher price and a higher quantity of turkey.

thus, in the short run firms will respond by increasing the price of turkey, selling more quantity at a higher price and earning economic profits.