What is the future value of a 5-year ordinary annuity with annual payments of $ 1,585 , evaluated at a 12.28 percent interest rate? Enter your answer to the nearest $.01. Do not use $ or , signs in your answer. Enter your answer as a positive number.



Answer :

Answer:

To calculate the future value of a 5-year ordinary annuity with annual payments of $1,585 at a 12.28% interest rate, you can use the future value of an ordinary annuity formula:

=

×

(

1

+

)

1

FV=P×

r

(1+r)

n

−1

where:

P is the annual payment ($1,585)

r is the annual interest rate (12.28% or 0.1228)

n is the number of periods (5 years)

Plugging in the values:

=

1585

×

(

1

+

0.1228

)

5

1

0.1228

FV=1585×

0.1228

(1+0.1228)

5

−1

First, calculate

(

1

+

)

(1+r)

n

:

(

1

+

0.1228

)

5

=

1.122

8

5

1.78737

(1+0.1228)

5

=1.1228

5

≈1.78737

Next, subtract 1:

1.78737

1

=

0.78737

1.78737−1=0.78737

Then, divide by

r:

0.78737

0.1228

6.412

0.1228

0.78737

≈6.412

Finally, multiply by the annual payment:

=

1585

×

6.412

10

,

159.22

FV=1585×6.412≈10,159.22

So, the future value of the annuity is approximately

10

,

159.22

10,159.22.