Present Value [2915]

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Assuming payments are made in advance, what is the present value of an ordinary annuity consisting of cash flows of $1,000.00 per year for the first five years, $2,000.00 per year for the next five years, and $3,000.00 per year for the final five years if a discount rate of six percent is appropriate?

 

Column

Rate

Years

Amount

Factor

Value

N/A

N/A

N/A

$1,000

1.000000

$1,000.00

5

6.0%

4

$1,000

3.465106

$3,465.11

5

6.0%

9

$2,000

6.801692

$13,603.38

5

6.0%

4

-$2,000

3.465106

-$6,930.21

5

6.0%

14

$3,000

9.294984

$27,884.95

5

6.0%

9

-$3,000

6.801692

-$20,405.08

 

 

 

 

 

$18,618.15

 

This is a 14-year annuity not a 15-year one.  The first year is paid in advance which means paid now.  In an annuity, the first payment is made at the end of the first period.

 

If an annuity starts after the first period, it is calculated as follows:

1.     Calculate the value of the annuity from the end of the first year until the last year.

2.     Calculate the value of the first year to the end of the year in which the annuity was not paid.

3.     Subtract the second from the first.

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