Answer:
You will pay approximately $1,341.76 in interest over the life of the loan.
Explanation:
To calculate your monthly payments on a $31,000 student loan with an interest rate of 5.85% compounded monthly and a goal to pay off the loan in 7 years, you can use the formula for the monthly payment of a fixed-rate mortgage or loan:
�
=
�
⋅
�
⋅
(
1
+
�
)
�
(
1
+
�
)
�
−
1
M=
(1+r)
n
−1
P⋅r⋅(1+r)
n
Where:
�
M is the monthly payment.
�
P is the principal amount (the loan amount, $31,000 in your case).
�
r is the monthly interest rate (annual interest rate divided by 12 months and converted to a decimal form).
�
n is the total number of payments (monthly payments for 7 years, which is
7
×
12
=
84
7×12=84 months).
Let's calculate it step by step:
Convert the annual interest rate to a monthly rate:
�
=
5.85
%
12
×
100
=
0.004875
r=
12×100
5.85%
=0.004875
Calculate the total number of payments:
�
=
7
×
12
=
84
n=7×12=84 months.
Now, plug these values into the formula:
�
=
31
,
000
⋅
0.004875
⋅
(
1
+
0.004875
)
84
(
1
+
0.004875
)
84
−
1
M=
(1+0.004875)
84
−1
31,000⋅0.004875⋅(1+0.004875)
84
Calculate the numerator first:
�
�
�
�
�
�
�
�
�
=
31
,
000
⋅
0.004875
⋅
(
1
+
0.004875
)
84
Numerator=31,000⋅0.004875⋅(1+0.004875)
84
�
�
�
�
�
�
�
�
�
≈
31
,
000
⋅
0.004875
⋅
1.655427423
Numerator≈31,000⋅0.004875⋅1.655427423
�
�
�
�
�
�
�
�
�
≈
252.812061
Numerator≈252.812061
Calculate the denominator:
�
�
�
�
�
�
�
�
�
�
�
=
(
1
+
0.004875
)
84
−
1
Denominator=(1+0.004875)
84
−1
�
�
�
�
�
�
�
�
�
�
�
≈
1.655427423
−
1
Denominator≈1.655427423−1
�
�
�
�
�
�
�
�
�
�
�
≈
0.655427423
Denominator≈0.655427423
Now, calculate the monthly payment:
�
=
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
≈
252.812061
0.655427423
≈
385.34
M=
Denominator
Numerator
≈
0.655427423
252.812061
≈385.34
So, your monthly payment will be approximately $385.34.
To find out how much interest you'll pay over the life of the loan, you can subtract the original principal from the total amount paid.
Total amount paid = Monthly payment * Number of payments = $385.34 * 84 ≈ $32,341.76
Interest paid = Total amount paid - Principal = $32,341.76 - $31,000 = $1,341.76
You will pay approximately $1,341.76 in interest over the life of the loan.