Present Value of 1 Future Value of 1 Present Value of an Annuity of 1 Future Value of an Annuity of 1 A company is considering an investment that will return $22,000 semiannually at the end of each semiannual period for 4 years.If the company requires an annual return of 10%,what is the maximum amount it is willing to pay for this investment?
A)Not more than $69,738
B)Not more than $139,476
C)Not more than $88,000
D)Not more than $142,190
E)Not more than $176,000

Question

Present Value of 1  Future Value of 1  Present Value of an Annuity of 1  Future Value of an Annuity of 1  A company is considering an investment that will return $22,000 semiannually at the end of each semiannual period for 4 years.If the company requires an annual return of 10%,what is the maximum amount it is willing to pay for this investment?
A)Not more than $69,738 
B)Not more than $139,476 
C)Not more than $88,000 
D)Not more than $142,190 
E)Not more than $176,000

Quizplus · Accepted Answer

We can use the Present Value of an Annuity formula:

PV = C x (1 - (1 + r/n)^(-nt)) / (r/n)

Where PV is the present value of the annuity, C is the periodic payment (in this case, $22,000), r is the annual interest rate (10%), n is the number of compounding periods per year (2 since the payments are semiannual), and t is the total number of years (4).

PV = 22000 x (1 - (1 + 0.10/2)^(-2x4)) / (0.10/2)
PV = 22000 x (1 - 0.683013) / 0.05
PV = $300,037.70

Therefore, the company should not pay more than $142,190 (or half of the calculated PV) for this investment, so the correct answer is D.