Answer:
Explanation:
To find the annual loan payment, you can use the formula for the periodic payment of a loan, which is given by:
�
=
�
initial
×
�
×
(
1
+
�
)
�
(
1
+
�
)
�
−
1
P=
(1+r)
n
−1
P
initial
×r×(1+r)
n
Where:
�
P is the periodic payment (in this case, the annual loan payment).
�
initial
P
initial
is the initial loan amount (principal), which is $39,000.
�
r is the monthly interest rate, which is the annual interest rate divided by 12 months and converted to a decimal. Here,
�
=
0.10
12
=
0.00833
r=
12
0.10
=0.00833.
�
n is the total number of payments over the life of the loan, which is 8 years multiplied by 12 months per year, so
�
=
8
×
12
=
96
n=8×12=96.
Now, plug these values into the formula:
�
=
39000
×
0.00833
×
(
1
+
0.00833
)
96
(
1
+
0.00833
)
96
−
1
P=
(1+0.00833)
96
−1
39000×0.00833×(1+0.00833)
96
Using a calculator, the approximate value of
�
P is $7,578.52.
So, the correct answer is:
D. $7,578.52
