FRL 300 Homework 4 (Chapter 6)

3. If you put up $50,000 today in exchange for a 6.75 percent, 14-year annuity, what will the annual cash flow be? (Do not round intermediate calculations and round your final answer to 2 decimal places, e.g., 32.16.) Annual cash flow $

annual cash flow pv=50,000 i=6.75 n=14 cpt, *pmt = 5631.84*

11. Beginning three months from now, you want to be able to withdraw $3,400 each quarter from your bank account to cover college expenses over the next four years. If the account pays .56 percent interest per quarter, how much do you need to have in your bank account today to meet your expense needs over the next four years? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Present value $

pmt = 3400 i = 0.56 n = 4x4 = 16 cpt, *pv = 51895.30*

10. One of your customers is delinquent on his accounts payable balance. You've mutually agreed to a repayment schedule of $500 per month. You will charge 2 percent per month interest on the overdue balance. If the current balance is $19,000, how long will it take for the account to be paid off? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Months for account to be paid off

pmt = 500 i = 2 fv = 19,000 cpt, *n = 72.07*

2. Cannonier, Inc., has identified an investment project with the following cash flows. Year Cash Flow 1 $ 1,080 2 1,310 3 1,530 4 2,270 If the discount rate is 9 percent, what is the future value of these cash flows in Year 4? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Future value $ What is the future value at a discount rate of 12 percent? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Future value $ What is the future value at a discount rate of 23 percent? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Future value $ ReferenceseBook & Resources WorksheetDifficulty: Basic

1080+1310+1530+2270 =6190 a. future value, i=9 CF0=0 C01=1080 F01=1 C02=1310 F02=1 C03=1530 F03=1 C04=2270 F04=1 NPV, I=9, CPT NPV = 4882.99 pv=4882.99... i=9 n=4 cpt *fv=6,892.74* b. future value, i=12 npv, i=12, cpt npv=4540.26 pv=4540.26 i=12 n=4 cpt *fv=7,144.19* c. future value, i=23 npv, i=23, cpt npv=3557.89 pv=3557.89 i=23 n=4 cpt *fv=8,143.54*

7. First National Bank charges 14.4 percent compounded monthly on its business loans. First United Bank charges 14.7 percent compounded semiannually. Calculate the EAR for First National Bank and First United Bank. (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) EAR: a. First National % b. First United % As a potential borrower, which bank would you go to for a new loan? c. First National Bank First United Bank

EAR = [ 1 + (APR/m)]^m -1 m = periods in one year a. EAR = [ 1 + (.144/12)]^12 -1 EAR = 15.39% b. EAR = [ 1 + (14.7/2)]^2 -1 EAR = 15.24% Lower interest rates are better for borrowers, so First United Bank is the preferred choice.

6. Find the EAR in each of the following cases (Use 365 days a year. Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.): Stated Rate (APR) Number of Times Compounded Effective Rate (EAR) 9.1 % Quarterly a. 18.1 Monthly b. 14.1 Daily c. 11.1 Infinite d.

EAR = [ 1 + (APR/m)]^m -1 m = periods in one year a. [ 1 + (.091/4)]^4 -1 EAR = 9.4% b. [ 1 + (.181/12)]^12 -1 EAR = 19.68% c. [ 1 + (.141/365)]^365 -1 EAR = 15.14% d. [ 1 + (.111/10,000)]^10,000 -1 EAR = 11.74%

1. Huggins Co. has identified an investment project with the following cash flows. Year Cash Flow 1 $ 910 2 1,310 3 1,570 4 1,750 a. If the discount rate is 11 percent, what is the present value of these cash flows? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Present value $ __________ b. What is the present value at 20 percent? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Present value $ __________ c. What is the present value at 30 percent? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Present value $ __________

a. CF: CFo = 0 C01 = 910 [ enter ] F01 = 1 C02 = 1310 [ enter ] F02 = 1 C03 = 1570 [ enter ] F03 = 1 C04 = 1750 [ enter ] F04 = 1 NPV: I = 11 [down arrow] [CPT] NPV *NPV = 4183.79* b. I = 20 *NPV = 3420.56* c. I = 30 *NPV = 2802.48*

12. You want to be a millionaire when you retire in 35 years. How much do you have to save each month if you can earn an annual return of 10.6 percent? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Savings per month $ How much do you have to save each month if you wait 10 years before you begin your deposits? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Savings per month $ How much do you have to save each month if you wait 20 years before you begin your deposits? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Savings per month $

a. n = 35 x 12 = 420 i = 10.6/12 = 0.88333 fv = 1,000,000 cpt, *pmt = 225.38* b. n = 25 x 12 = 300 cpt, *pmt = 679.99* c. n = 15 x 12 = 180 cpt, *pmt = 2282.73*

13. Suppose you are going to receive $14,100 per year for six years. The appropriate interest rate is 6.9 percent. What is the present value of the payments if they are in the form of an ordinary annuity? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Present value $ What is the present value if the payments are an annuity due? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Present value $ Suppose you plan to invest the payments for six years. What is the future value if the payments are an ordinary annuity? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Future value $ Suppose you plan to invest the payments for six years. What is the future value if the payments are an annuity due? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Future value $

a. pmt = 14,100 n = 6 i = 6.9 cpt, *pv = 67,416.19* b. 2nd, BGN, 2nd, SET -now in bgn mode- cpt, *pv = 72,067.91* exit bgn mode c. pmt = 14,100 n = 6 i = 6.9 cpt, *fv = 100,607* d. 2nd, BGN, 2nd, SET -now in bgn mode- cpt, *fv = 107,549.44* exit bgn mode

4. If you deposit $5,300 at the end of each of the next 20 years into an account paying 10.8 percent interest, how much money will you have in the account in 20 years? (Do not round intermediate calculations and round your final answer to 2 decimal places, e.g., 32.16.) Future value $ How much will you have if you make deposits for 40 years? (Do not round intermediate calculations and round your final answer to 2 decimal places, e.g., 32.16.) Future value $

a. pmt=5300 n=20 i=10.8 cpt, *fv = 332,560.16* b. n=40 cpt, *fv = 2,918,779.91*

8. Big Dom's Pawn Shop charges an interest rate of 26.4 percent per month on loans to its customers. Like all lenders, Big Dom must report an APR to consumers. What rate should the shop report? (Do not round intermediate calcualtions. Enter your answer as a percent rounded to 1 decimal place, e.g., 32.1.) APR % What is the effective annual rate? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) EAR %

a. APR = Interest rate x # of periods = 26.4% x 12 *APR = 316.8%* b. EAR = [ 1 + (APR/m)]^m -1 = [ 1 + (3.168/12)]^12 -1 = 15.6328 *EAR = 1563.28%*

9. You want to buy a new sports coupe for $85,500, and the finance office at the dealership has quoted you an APR of 6.7 percent for a 72 month loan to buy the car. What will your monthly payments be? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Monthly payment $ What is the effective annual rate on this loan? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Effective annual rate %

a. monthly payment i = 6.7/12 = 0.55833 n=72 pv=85,500 cpt, *pmt = 1445.40* b. EAR (72 month /12 = 6 yr) = [ 1 + (APR/m)]^m -1 = [ 1 + (.067/6)]^6 -1 = *6.89%*

5. The Maybe Pay Life Insurance Co. is trying to sell you an investment policy that will pay you and your heirs $20,000 per year forever. If the required return on this investment is 5.3 percent, how much will you pay for the policy? (Do not round intermediate calculations. Round your answer to 2 decimal places, e.g., 32.16.) Present value $

present value pmt=20,000 i=5.3 n= PICK A RIDICULOUSLY LARGE NUMBER, like 10,000 cpt *pv = 377,358.49*