Respuesta :
Answer:
Therefore, the approximate monthly payment is $548.85
Step-by-step explanation:
The amount of student loans Erica currently has = $34,006.00
The duration over which Erica is to pay back the loan = 7 years
The annual interest rate for the loan = 9.1%
Therefore, we have the geometric sequence formula is given as follows;
[tex]A_n = P( 1 + r)^n - M \times \left [ \dfrac{(1 + r)^n-1}{r} \right ][/tex]
Where;
M = The monthly payment
P = The initial loan balance = $34,006.00
r = The annual interest rate = 9.1%
n = The number of monthly payment = 7 × 12 = 84
Aₙ = The amount remaining= 0 at the end of the given time for payment
Substituting the values into the above formula, , we get;
[tex]0 = 34006 \times \left ( 1 + \dfrac{0.091}{12} \right )^{84} - M \times \left [ \dfrac{\left (1 + \dfrac{0.091}{12} \right )^{84}-1}{\dfrac{0.091}{12} } \right ][/tex]
[tex]M = \dfrac{34006 \times \left ( 1 + \dfrac{0.091}{12} \right )^{84} }{\left [ \dfrac{\left (1 + \dfrac{0.091}{12} \right )^{84}-1}{\dfrac{0.091}{12} } \right ]} \approx 548.85[/tex]
Therefore, the approximate monthly payment = $548.85
