Annuity

Use the following information in answering Cases 1 and 2 below.

On January 1, 2001, Carr Company sold $600,000 of 10% bonds, due January 1, 2011. Interest on these bonds is paid on July 1 and January 1 each year. According to the terms of the bond contract, Carr must establish a sinking fund for the retirement of the bond principal starting no later than January 1, 2009. Since Carr was in a tight cash position during the years 2001 through 2006, the first contribution into the fund was made on January 1, 2007.

Case 1: Assume that, starting with the January 1, 2007 contribution, Carr desires to make a total of four equal annual contributions into this fund. Compute the amount of each of these contributions assuming the interest rate is 8% compounded annually.

Case 2: On January 2, 2007, Milton Company loaned $80,000 to Renn Company. The terms of this loan agreement stipulate that Renn is to make 5 equal annual payments to Milton at 10% interest compounded annually. Assume the payments are to begin on December 31, 2007. Compute the amount of each of these payments.

In computing your answers to the cases below, you can round your answer to the nearest dollar. Present value tables are provided on the next page.

Table 1

Future Value of 1

Periods 6% 8% 9% 10% 12%

1 1.06000 1.08000 1.09000 1.10000 1.1200

2 1.12360 1.16640 1.18810 1.21000 1.2544

3 1.19102 1.25971 1.29503 1.33100 1.4049

4 1.26248 1.36049 1.41158 1.46410 1.5735

5 1.33823 1.46933 1.53862 1.61051 1.7623

Table 2

Present Value of 1

Periods 6% 8% 9% 10% 12%

1 0.94340 0.92593 0.91743 0.90909 0.8928

2 0.89000 0.85734 0.84168 0.82645 0.7971

3 0.83962 0.79383 0.77218 0.75132 0.7117

4 0.79209 0.73503 0.70843 0.68301 0.6355

5 0.74726 0.68058 0.64993 0.62092 0.5674

Table 3

Future Value of an Ordinary Annuity of 1

Periods 6% 8% 9% 10% 12%

1 1.00000 1.00000 1.00000 1.00000 1.0000

2 2.06000 2.08000 2.09000 2.10000 2.1200

3 3.18360 3.24640 3.27810 3.31000 3.3744

4 4.37462 4.50611 4.57313 4.64100 4.7793

5 5.63709 5.86660 5.98471 6.10510 6.3528

Table 4

Present Value of an Ordinary Annuity of 1

Periods 6% 8% 9% 10% 12%

1 0.94340 0.92593 0.91743 0.90909 0.8928

2 1.83339 1.78326 1.75911 1.73554 1.6900

3 2.67301 2.57710 2.53130 2.48685 2.4018

4 3.46511 3.31213 3.23972 3.16986 3.0373

5 4.21236 3.99271 3.88965 3.79079 3.6047

Table 5

Present Value of an Annuity Due of 1

Periods 6% 8% 9% 10% 12%

1 1.00000 1.00000 1.00000 1.00000 1.0000

2 1.94340 1.92593 1.91743 1.90909 1.8928

3 2.83339 2.78326 2.75911 2.73554 2.6900

4 3.67301 3.57710 3.53130 3.48685 3.4018

5 4.46511 4.31213 4.23972 4.16986 4.0373