Answer:
To calculate the future value of a deposit compounded semi-annually, you can use the formula for compound interest:
�
=
�
(
1
+
�
�
)
�
�
A=P(1+
n
r
)
nt
Where:
�
A is the future value of the deposit.
�
P is the initial deposit amount ($18,000 in this case).
�
r is the annual interest rate (5% or 0.05 as a decimal).
�
n is the number of times the interest is compounded per year (semi-annually means 2 times per year).
�
t is the number of years the money is invested (10 years in this case).
Now, plug in the values and calculate:
�
=
18
,
000
(
1
+
0.05
2
)
2
⋅
10
A=18,000(1+
2
0.05
)
2⋅10
�
=
18
,
000
(
1
+
0.025
)
20
A=18,000(1+0.025)
20
�
=
18
,
000
×
1.02
5
20
A=18,000×1.025
20
Using a calculator, you can find that
1.02
5
20
≈
1.282037
1.025
20
≈1.282037.
Now, multiply:
�
≈
18
,
000
×
1.282037
≈
23
,
076.67
A≈18,000×1.282037≈23,076.67
So, there will be approximately $23,076.67 in the fund after 10 years.