Question

If $9,000 is invested in a certain business at the start of the​ year, the investor will receive $2,700 at the end of each of the next four years. What is the present value of this business opportunity if the interest rate is 7​% per​ year?

A. $73

B. $145

C. $233

D. $175

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An investment pays you ​$20,000 at the end of this​ year, and $10,000 at the end of each of the four following years. What is the present value​ (PV) of this​ investment, given that the interest rate is 4​% per​ year?

A. $27,067

B. $54,134

C. $43,307

D. $64,961

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A perpetuity has a PV of $40,000. If the interest rate is 9​%, how much will the perpetuity pay every​ year?

A. $2,880

B. $3,600

C. $2,160

D $1,800

Answer 1

Answer to Question 1 is $145:

Amount Invested = $9,000
Annual Receipt = $2,700
Time Period = 4 years
Interest Rate = 7%

Present Value = -$9,000 + $2,700/1.07 + $2,700/1.07^2 + $2,700/1.07^3 + $2,700/1.07^4
Present Value = -$9,000 + $2,700 * (1 - (1/1.07)^4) / 0.07
Present Value = -$9,000 + $2,700 * 3.387211
Present Value = $145

Answer to Question 2 is $54,134:

Cash Flow, Year 1 = $20,000
Cash Flow, Year 2 = $10,000
Cash Flow, Year 3 = $10,000
Cash Flow, Year 4 = $10,000
Cash Flow, Year 5 = $10,000

Interest Rate = 4%

Present Value = $20,000/1.04 + $10,000/1.04^2 + $10,000/1.04^3 + $10,000/1.04^4 + $10,000/1.04^5
Present Value = $54,134

Answer to Question 3 is $3,600:

Present Value of Perpetuity = Annual Payment / Interest Rate
$40,000 = Annual Payment / 0.09
Annual Payment = $3,600