An employer wants to pay $400 every 6 months to a deserving employee forever.The company has $A to fund the award and can earn j₂ = 8%.If the first award is to be paid out 3 months from now,what is A? (Answer to nearest dollar)

Question

Quizplus · Accepted Answer

To calculate A, we can use the formula for the perpetuity:

PV = PMT / i

where PV is the present value of the perpetuity, PMT is the payment made every period, and i is the interest rate.

In this case, we have PMT = $400 every 6 months, or $800 per year. We also have i = 8% per year, or 4% every 6 months.

To find PV, we need to discount the perpetuity back to today by 3 months, at a rate of 4% per 6 months. Using the formula for present value with continuous compounding:

PV = PMT / (i * e^(i*t))

where t is the time in years, or in this case, 0.25 years (3 months out of 12).

PV = $800 / (0.04 * e^(0.04*0.25)) = $10,198.31

Therefore, the closest answer choice is C, $10,198.

An Employer Wants to Pay $400 Every 6 Months to a Deserving