Answer:
29,141
Step-by-step explanation:
To find the value of the account at the child's twenty-first birthday, we can use the formula for compound interest:
�
=
�
×
(
1
+
�
�
)
�
�
A=P×(1+
n
r
)
nt
Where:
�
A is the amount of money accumulated after
�
t years, including interest.
�
P is the principal amount (the initial amount of money).
�
r is the annual interest rate (in decimal).
�
n is the number of times that interest is compounded per year.
�
t is the time the money is invested for, in years.
Given:
P = $7000
�
=
8.5
%
=
0.085
r=8.5%=0.085 (as a decimal)
�
=
12
n=12 (compounded monthly)
�
=
21
t=21 years
Let's plug these values into the formula:
�
=
7000
×
(
1
+
0.085
12
)
12
×
21
A=7000×(1+
12
0.085
)
12×21
�
=
7000
×
(
1
+
0.085
12
)
252
A=7000×(1+
12
0.085
)
252
Now, let's calculate the expression inside the parentheses first:
1
+
0.085
12
=
1
+
0.085
12
1+
12
0.085
=1+
12
0.085
=
1
+
0.0070833
=1+0.0070833
≈
1.0070833
≈1.0070833
Now, let's raise this value to the power of
252
252:
≈
(
1.0070833
)
252
≈(1.0070833)
252
≈
4.163
≈4.163
Now, let's plug this back into the original formula:
�
≈
7000
×
4.163
A≈7000×4.163
�
≈
29141
A≈29141
So, the value of the account at the child's twenty-first birthday will be approximately $29,141.
