Use the following time value of money tables to answer the following questions. Assume that the annual rate of interest is 6% for each of the four following problems.

i = 6%
Time Periods (n)
Future Value
of 1 Present Value
of 1 Future Value of an Annuity Present Value of an Annuity
3 1.19102 .83962 3.18360 2.67301

i = 3%
Time Periods (n)
Future Value
of 1 Present Value
of 1 Future Value of an Annuity Present Value of an Annuity
6 1.19405 .83748 6.46841 5.41719

1. Determine the future value of a $2,000 deposit made on January 1, 2011 on December 31, 2013 if the bank compounds interest annually.

2. Compute the present value of an amount of money on January 1, 2011 if its future value is $5,000 on December 31, 2013 and interest compounds semiannually.

3. Calculate the future value of a $1,000 annuity on December 31, 2013 if the firm makes annual deposits on December 31, 2011, December 31, 2012, and December 31, 2013.

4. Determine the present value on January 1, 2011 of $500 annuity payments made on each June 30 and December 31 from 2011 through 2013.

To answer these questions, we will be using the time value of money tables provided. Specifically, we will be using the "Future Value of 1", "Present Value of 1", "Future Value of an Annuity", and "Present Value of an Annuity" tables.

1. To determine the future value of a $2,000 deposit made on January 1, 2011, on December 31, 2013, we need to find the appropriate factor in the "Future Value of 1" table for a 3-year period at an interest rate of 6%. The factor is 1.19102. We can multiply this factor by the $2,000 deposit to get the future value:

Future Value = $2,000 * 1.19102 = $2,382.04

Therefore, the future value of the $2,000 deposit made on January 1, 2011, on December 31, 2013, will be $2,382.04.

2. To compute the present value of an amount of money on January 1, 2011, if its future value is $5,000 on December 31, 2013, and interest compounds semiannually, we need to find the appropriate factor in the "Present Value of 1" table for a 4-year period (8 semiannual periods) at an interest rate of 3%. The factor is 0.83748. We can divide the $5,000 future value by this factor to get the present value:

Present Value = $5,000 / 0.83748 = $5,981.15

Therefore, the present value of an amount of money on January 1, 2011, with a future value of $5,000 on December 31, 2013, and interest compounding semiannually, will be $5,981.15.

3. To calculate the future value of a $1,000 annuity on December 31, 2013, if the firm makes annual deposits on December 31, 2011, December 31, 2012, and December 31, 2013, we need to find the appropriate factor in the "Future Value of an Annuity" table for a 3-year period at an interest rate of 6%. The factor is 3.18360. We can multiply this factor by the $1,000 annuity payment to get the future value:

Future Value = $1,000 * 3.18360 = $3,183.60

Therefore, the future value of the $1,000 annuity on December 31, 2013, with annual deposits made on December 31, 2011, December 31, 2012, and December 31, 2013, will be $3,183.60.

4. To determine the present value on January 1, 2011, of $500 annuity payments made on each June 30 and December 31 from 2011 through 2013, we need to find the appropriate factor in the "Present Value of an Annuity" table for a 3-year period at an interest rate of 6%. The factor is 2.67301. We can multiply this factor by the $500 annuity payment to get the present value:

Present Value = $500 * 2.67301 = $1,336.51

Therefore, the present value on January 1, 2011, of $500 annuity payments made on each June 30 and December 31 from 2011 through 2013 will be $1,336.51.

1. To determine the future value of a $2,000 deposit made on January 1, 2011, on December 31, 2013, if the bank compounds interest annually, use the "Future Value of 1" table.

Since the time period is 3 years, the future value factor is 1.19102 (from the table). Multiply the deposit amount by the future value factor:

Future Value = $2,000 * 1.19102 = $2,382.04

Therefore, the future value of the $2,000 deposit made on January 1, 2011, on December 31, 2013, is $2,382.04.

2. To compute the present value of an amount of money on January 1, 2011, if its future value is $5,000 on December 31, 2013, and interest compounds semiannually, use the "Present Value of 1" table.

Since the time period is 6 years, the present value factor is 0.83748 (from the table). Divide the future value by the present value factor:

Present Value = $5,000 / 0.83748 = $5,977.26

Therefore, the present value of the amount of money on January 1, 2011, is $5,977.26.

3. To calculate the future value of a $1,000 annuity on December 31, 2013, if the firm makes annual deposits on December 31, 2011, December 31, 2012, and December 31, 2013, use the "Future Value of an Annuity" table.

Since the time period is 3 years, the future value of an annuity factor is 3.18360 (from the table). Multiply the annuity amount by the future value of an annuity factor:

Future Value = $1,000 * 3.18360 = $3,183.60

Therefore, the future value of the $1,000 annuity on December 31, 2013, is $3,183.60.

4. To determine the present value on January 1, 2011, of $500 annuity payments made on each June 30 and December 31 from 2011 through 2013, use the "Present Value of an Annuity" table.

Since the time period is 3 years, the present value of an annuity factor is 2.67301 (from the table). Multiply the annuity payment by the present value of an annuity factor:

Present Value = $500 * 2.67301 = $1,336.50

Therefore, the present value on January 1, 2011, of $500 annuity payments made on each June 30 and December 31 from 2011 through 2013 is $1,336.50.