FIN 300 Chapter 5

Alfa Life Insurance Co. is trying to sell you an investment policy that will pay you and your heirs $10,000 per year forever. If the guaranteed rate of return on this investment is 3.6 percent, how much will you pay for the policy? A. $266,576.83 B. $277,777.78 C. $254,211.50 D. $267,119.02 E. $241,160.91

B. $277,777.78 PV = $10,000/.036 = $277,777.78

oday, you are purchasing a 20-year, 6 percent annuity at a cost of $48,350. The annuity will pay annual payments starting one year from today. What is the amount of each payment? A. $4,511.08 B. $4,215.37 C. $2,754.40 D. $4,013.20 E. $5,208.19

B. $4,215.37 *PV = $48,350 = C × {1 - [1 / (1 + .06)20]} / .06 C = $4,215.37*

Good Guys will pay you $3,800 a year for 10 years in exchange for $31,300 today. What interest rate will you earn on this annuity? A. 1.67 percent B. 3.69 percent C. 5.50 percent D. 2.55 percent E. 2.38 percent

B. 3.69 percent *PV = $31,300 = $3,800 × {1 - [1 / (1 + r)10]} / r r = 3.69 percent*

You want to purchase a new condominium that costs $287,500. Your plan is to pay 25 percent down in cash and finance the balance over 15 years at 3.75 percent. What will be your monthly mortgage payment including principal and interest? A. $1,568.07 B. $1,333.33 C. $1,708.16 D. $1,221.43 E. $1,406.11

A. $1,568.07 *Amount financed = (1 - .25) ×$287,500 = $215,625 PV = $215,625 = C × (1 - {1 / [1 + (.0375 / 12)]180}) / (.0375 / 12) C = $1,568.07*

You want to purchase a new condominium that costs $287,500. Your plan is to pay 25 percent down in cash and finance the balance over 15 years at 3.75 percent. What will be your monthly mortgage payment including principal and interest? A. $1,568.07 B. $1,333.33 C. $1,708.16 D. $1,221.43 E. $1,406.11

A. $1,568.07 Amount financed = (1 - .25) ×$287,500 = $215,625 PV = $215,625 = C × (1 - {1 / [1 + (.0375 / 12)]180}) / (.0375 / 12) C = $1,568.07

What is the effective annual rate of 9.6 percent compounded semiannually? A. 9.71 percent B. 9.83 percent C. 9.79 percent D. 9.68 percent E. 9.92 percent

B. 9.83 percent EAR = [1 + (.096 /2)]2- 1 = .0983, or 9.83 percent

Janis just won a scholarship that will pay her $500 a month, starting today, and continuing for the next 48 months. Which one of the following terms best describes these scholarship payments? A. Ordinary annuity B. Annuity due C. Consol D. Ordinary perpetuity E. Perpetuity due

B. Annuity due

The manager of Gloria's Boutique has approved Carla's application for 24 months of credit with maximum monthly payments of $70.If the APR is 14.2 percent, what is the maximum initial purchase that Carla can buy on credit? A. $1,006.90 B. $1,300.00 C. $1,455.08 D. $1,184.75 E. $1,228.46

C. $1,455.08 *PV = $70 × (1 - {1 / [1 + (.142 / 12)]24}) / (.142 / 12) = $1,455.08*

Today, you are borrowing $7,800 to purchase a car. What will be your monthly payment if the loan is for four years at 6.45 percent interest? A. $208.40 B. $221.50 C. $184.80 D. $180.24 E. $200.10

C. $184.80 PV = $7,800 = C ×[(1 - {1 / [1 + (.0645 / 12)]48}) / (.0645 / 12)]

Suenette plans to save $600 at the end of Year 1, $800 at the end of Year 2, and $1,000 at the end of Year 3. If she earns 3.4 percent on her savings, how much money will she have saved at the end of Year 3? A. $2,200.00 B. $2,238.47 C. $2,468.69 D. $2,309.16 E. $2,402.19

C. $2,468.69 FV = ($600 ×1.0342) + ($800 ×1.0341) + $1,000 = $2,468.69

Capstone Investments is considering a project that will produce cash inflows of $11,000 at the end of Year 1, $24,000 in Year 2, and $36,000 in Year 3. What is the present value of these cash inflows at a discount rate of 12 percent? A. $41,997.60 B. $46,564.28 C. $54,578.17 D. $54,868.15 E. $63,494.54

C. $54,578.17 PV = ($11,000/1.12) + ($24,000/1.122) + ($36,000/1.123) = $54,578.17

You plan to save $200 a month for the next 24 years and hope to earn an average rate of return of 10.6 percent. How much more will you have at the end of the 24 years if you invest your money at the beginning rather than the end of each month? A. $1,911.29 B. $1,807.70 C. $2,238.87 D. $2,317.82 E. $2,707.27

D. $2,317.82 *FV = $200 × {[1 + (.106 / 12)]288 - 1} / (.106 / 12) = $262,394.25 Difference = {$262,394.25 × [1 + (.106 / 12)]} - $262,394.25 = $2,317.82*

Eric is considering an investment that will pay $8,200 a year for five years, starting one year from today. What is the maximum amount he should pay for this investment if he desires a rate of return of 11.2 percent? A. $17,899.08 B. $27,117.36 C. $20,186.75 D. $30,154.50 E. $18,153.55

D. $30,154.50 *PV = $8,200 ×{1 - [1 / (1 + .112)5]} / .112 = $30,154.50*

Which one of the following has the highest effective annual rate? A.6 percent compounded annually B. 6 percent compounded semiannually C. 6 percent compounded quarterly D. 6 percent compounded daily E. 6 percent compounded every 2 years

D. 6 percent compounded daily

Which statement is true? A. All else equal, an ordinary annuity is more valuable than an annuity due. B. All else equal, a decrease in the number of payments increases the future value of an annuity due. C. An annuity with payments at the beginning of each period is called an ordinary annuity. D. All else equal, an increase in the discount rate decreases the present value and increases the future value of an annuity. E. All else equal, an increase in the number of annuity payments decreases the present value and increases the future value of an annuity.

D. All else equal, an increase in the discount rate decreases the present value and increases the future value of an annuity.

Chandler Tire Co. is trying to decide which one of two projects it should accept. Both projects have the same start-up costs. Project 1 will produce annual cash flows of $52,000 a year for six years. Project 2 will produce cash flows of $48,000 a year for eight years. The company requires a 15 percent rate of return. Which project should the company select and why? A. Project 1, because the annual cash flows are greater by $4,000 than those of Project 2 B. Project 1, because the present value of its cash inflows exceeds those of Project 2 by $14,211.62 C. Project 2, because the total cash inflows are $72,000 greater than those of Project 1 D. Project 2, because the present value of the cash inflows exceeds those of Project 1 by $18,598.33 E. It does not matter as both projects have almost identical present values.

D. Project 2, because the present value of the cash inflows exceeds those of Project 1 by $18,598.33 *PV1 = $52,000 ×{1 -[1 / (1 + .15)6]} / .15 = $196,793.10 PV2 = $48,000 ×{1 -[1 / (1 + .15)8]} / .15 = $215,391.43 Difference = $215,391.43 - 196,793.10 = $18,598.33*

Christie is buying a new car today and is paying a $500 cash down payment. She will finance the balance at 6.3 percent interest. Her loan requires 36 equal monthly payments of $450 each with the first payment due 30 days from today. Which one of the following statements is correct concerning this purchase? A. The present value of the car is equal to $500 + (36 ×$450). B. The $500 is the present value of the purchase. C. The car loan is an annuity due. D. To compute the initial loan amount, you must use a monthly interest rate. E. The future value of the loan is equal to 36 ×$450.

D. To compute the initial loan amount, you must use a monthly interest rate.

How much money does Suzie need to have in her retirement savings account today if she wishes to withdraw $42,000 a year for 25 years? She expects to earn an average rate of return of 9.75 percent. A. $426,580.50 B. $407,419.81 C. $401,533.33 D. $385,160.98 E. $388,683.83

E. $388,683.83 PV = $42,000 ×{1 - [1 / (1 + .0975)25]} / .0975 = $388,683.83

Overnight Trucking recently purchased a new truck costing $219,800. The firm financed this purchase at 6.6 percent interest with monthly payments of $2,435. How many years will it take the firm to pay off this debt? A. 11.04 years B. 9.22 years C. 11.60 years D. 10.23 years E. 10.42 years

E. 10.42 years *PV = $219,800 = $2,435 × (1 - {1 / [1 + (.066 / 12)]t}) / (.066 / 12) t = 125.09 months Years = 125.09 / 12 = 10.42 years*

City Motors will sell a $15,000 car for $345 a month for 52 months. What is the interest rate? A. 9.28 percent B. 8.67 percent C. 8.53 percent D. 9.10 percent E. 8.38 percent

E. 8.38 percent PV = $15,000 = $345 × (1 - {1 / [1 + (r / 12)]52}) / (r / 12) r = 8.38 percent