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.
