All questions are answered. Please check and if needed correct any inaccurate answers, thank you!

1. Mrs. Beach wants to invest a lump sum of money today to have $100,000 when she retires at 65 (she is 40 today).

a. How much of a deposit would she have to make if the interest rate on the C.D. was 5%?

Present value = future value / (1 + rate of interest) ^n

= 100,000 / (1 + 5%) ^25

= $29,530.28

b. What would Mrs. Beach have to deposit if she were to use high quality corporate bonds an earned an average rate of return of 7%.

Present value = future value / (1 + rate of interest) ^n

= 100,000 / (1 + 7%) ^25

= $18,424.92

c. What would Mrs. Beach have to deposit if she were to use common stock and earned an average rate of return of 11%.

Present value = future value / (1 + rate of interest) ^n

= 100,000 / (1 + 11%) ^25

= $7,360.81

d. What type of a problem is this? Time value of money or growth value

2. You have a payment that is due in 5 years for $50,000. You can earn a 5% safe rate of return on your money.

a. How much would you have to set aside today meet this payment in the Future?

Present value = future value / (1 + rate of interest) ^n

= 50,000 / (1 + 5%) ^5

= $39,716.31

b. If your rate of return is 8%, how much would you have to set aside today?

Present value = future value / (1 + rate of interest) ^n

= 50,000 / (1 + 8%) ^5

= $34,209.16

c. If your rate of return is 10%, how much would you have to set aside today?

Present value = future value / (1 + rate of interest) ^n

= 50,000 / (1 + 10%) ^5

= $31,046.07

d. What type of a problem is this? Future Value.

3. You want to save enough money to retire as a millionaire.

a. If you could earn 10% with common stocks, how much would you have to set aside per year to have $1,000,000 when you are 65?

Present value = future value / (1 + rate of interest) ^n

= 1,000,000 / (1 + 10%) ^39

= $2,490.98

b. If you were going to make deposit monthly, how much would you have to set aside per month to have $1,000,000 when you are 65?

Present value = future value / (1 + rate of interest) ^n

= 1,000,000 / (1 + .83%) ^468

= $175.03

c. If you were able to earn 11%, how much would you have to set aside per month to have $1,000,000 when you are 65?

Present value = future value / (1 + rate of interest) ^n

= 1,000,000 / (1 + .92%) ^468

= $129.92

d. What type of a problem is this? Annuity Calculator.

4. If you were going to buy your office from Mrs. Beach for $500,000 with a 10% down payment and 15 years with a 6% interest rate.

a. How much would your payments be each month?

Present value = future value / (1 + rate of interest) ^n

= 450,000 / (1 + .50%) ^180

= $3,797,36

b. What would be the principal and interest payment on the first payment?

Principal: $1,547.36

Interest: $2,250.00

c. What would be the principal and interest payment on the twelfth payment?

Payment # Interest Principal Balance

1 2,250 1547.36 448452.64

2 2242.26 1555.09 446897.55

3 2234.49 1562.87 445334.68

4 2226.67 1570.68 443764.00

5 2218.82 1578.54 442185.46

6 2210.93 1578.54 440606.93

7 2203.03 1594.32 439012.60

8 2195.06 1602.29 437410.31

9 2187.05 1610.30 435800.01

10 2179.00 1618.36 434181.65

11 2170.91 1626.45 432010.74

12 2160.05 1637.30 429850.69

Interest: $2,160.05

Principal: $1,637.30

d. What type of a problem is this? Present value of annuity.

5. Same problem as above, but assume that the loan was for 20 years?

a. What is the new payment?

Present value = future value / (1 + rate of interest) ^n

= 450,000 / (1 + .50%) ^240

= $3,223.94

b. What would be the principal and interest payment on the first payment?

Principal: $973.94

Interest: $2,250.00

c. What would be the principal and interest payment on the twelfth payment?

Payment # Interest Principal Balance

1 2,250 973.94 449026.06

2 2245.13 978.81 448047.25

3 2240.24 983.70 447063.55

4 2235.32 988.62 446074.93

5 2230.37 993.57 445081.36

6 2225.41 998.53 444082.83

7 2220.41 1003.53 443079.30

8 2215.40 1008.54 442070.76

9 2210.35 1013.59 441057.17

10 2205.29 1018.65 440038.52

11 2200.19 1023.75 439014.77

12 2195,07 1028.87 437985.91

Interest: $2,195.07

Principal: $1,028.87

d. What type of a problem is this? Present value of annuity.

6. You want to purchase a truck for $25,000 and you have $3,450 to put down.

a. How much will your payments be if you financed the truck for 60 months at 6%?

Present value = future value / (1 + rate of interest) ^n

= 2,1550 / (1 + .50%) ^60

= $416.62

b. How much would the payment be if rate of interest is 5% and you only financed the truck for 48 months?

Present value = future value / (1 + rate of interest) ^n

= 2,1550 / (1 + .42%) ^48

= $496.28

c. Assuming that you would only finance the truck for 4 years, how much would you need to put down to get your payment to $450.00?

Present value = future value / (1 + rate of interest) ^n

= 19,540.33 / (1 + .42%) ^48

= $450

d. What type of a problem is this? Present value of annuity.

7. You have $350.00 per month to spend on a car payment. If your credit union charged 7.5% interest on a used car, how much car can you purchase if you will only finance for 4 years? __________

Present value = future value / (1 + rate of interest) ^n

= 14,475.43 / (1 + .00625%) ^48

= $350

8. If you want to purchase a factory. You have $50,000 to put down. All you can afford is $1500.00 per month and you do not want to finance for more than 15 years @ 6.5%, (your taxes will be $185.00 per month and insurance $600.00 a month), what is the amount you can pay for the house? (Show all your work)

Present value = future value / (1 + rate of interest) ^n

= 82,079.43 / (1 + .0054166667%) ^180

= $715

$132,079.43

9. You want to purchase a business with the following cash flows. How much would you pay for this business today assuming you need a 14% return to make this deal? a. First year $150,000 b. Second year $175,000 c. Third year $225,000 d. Forth year $275,000

$580,926.43

10. How much would you pay for this business today assuming you needed a 18% return to make this deal? (Same problem as above.)

$531,584.81

What type of a problem is this? Present value.