1.If you increase the number of payments on an amortized loan, does the payment increase or decrease? Explain.

2.Different cash flow. Given the following cash inflow at the end of each year, what is the future value of this cash flow at 6%, 9%, and 15% interest rates at the end of the seventh year?

Year 1$15,000

Year 2 $20,000

Year 3 $30,000

Years 4 through 6 $0

Year 7 $150,000

3.Future value of an ordinary annuity. Fill in the missing future values in the following table for an ordinary annuity.

4.Different cash flow. Given the following cash inflow, what is the present value of this cash flow at 5%, 10%, and 25% discount rates?

Year 1: $3,000

Year 2: $5,000

Years 3 through 7: $0

Year 8: $25,000

5. Present value of an ordinary annuity. Fill in the missing present values in the following table for an ordinary annuity.

Number of Payments or Years

Annual Interest Rate

Future Value

Annuity

Present Value

10

6%

0

$250.00

20

12%

0

$3,387.88

25

4%

0

$600.00

360

1%

0

$2,571.53

6. Ordinary annuity payment. Fill in the missing annuity in the following table for an ordinary annuity stream.

Number of Payments or Years

Annual Interest Rate

Future Value

Annuity

Present Value

5

9%

0

$25,000.00

20

8%

$25,000.00

0

30

7%

0

$200,000.00

10

4%

$96,048.86

0

7.County Ranch Insurance Company wants to offer a guaranteed annuity in units of $500, payable at the end of each year for twenty-five years. The company has a strong investment record and can consistently earn 7% on its investments after taxes. If the company wants to make 1% on this contract, what price should it set on it? Use 6% as the discount rate. Assume that it is an ordinary annuity and that the price is the same as present value.

8.Annuity due. Reginald is about to lease an apartment for the year. The landlord wants the lease payments paid at the start of the month. The twelve-monthly payments are $1,300 per month. The landlord says he will allow Reginald to prepay the rent for the entire year with a discount. The one-time annual payment due at the beginning of the lease is $14,778. What is the implied monthly discount rate for the rent? If Reginald is earning 1.5% on his savings monthly, should he pay by month or take the one annual payment?

9. Perpetuities. The Stack has just written and recorded the single greatest rock song ever made. The boys in the band believe that the royalties from this song will pay the band a handsome $200,000 every year forever. The record studio is also convinced that the song will be a smash hit and that the royalty estimate is accurate. The record studio wants to pay the band upfront and not make any more payments for the song. What should the record company offer the band if they use a 5% discount rate, a 7.5% discount rate, or a 10% discount rate?

10.Amortization. Loan Consolidated Incorporated (LCI) is offering a special one-time package to reduce Custom Autos' outstanding bills to one easy-to-handle payment plan. LCI will pay off the current outstanding bills of $242,000 for Custom Autos if Custom Autos will make an annual payment to LCI at a 10% interest rate over the next fifteen years. First, what are the annual payments and the remaining balance of the loan at the end of each year (should Custom Autos want to pay off the loan early)? Second, when will the balance be half paid off? Finally, what is the total interest expense on the loan over the fifteen years?

Payment = $242,000 / [(1 - 1/1.10¹⁵) / 0.10] = $242,000 / 7.6060 = $31,816.65

Amortization Schedule with Interest per period based on beginning balance 0.15

Year

Beg. Balance

Payment

Interest

Principal Reduction

Ending Balance

1

$242,000.00

$234,383.35

2

$234,383.35

3

4

5

6

7

8

9

10

11

12

13

14

15

Total

__________

The loan balance will be half-way paid off at the end of the tenth year or two thirds the way through the contract. The total interest expense over the contract is $______________________.