Question

After four years of college, Erica has to start paying off all her student loans. Her first payment is due at the end of this month. Her bank told her that she has 7 years to pay off all of her loans, and that starting this month, the loans will be compounded monthly at a fixed annual rate of 9.1%. Erica currently has a total of $34,006.00 in student loans. Use the formula for the sum of a finite geometric sequence to determine Erica's approximate monthly payment.

Answer 1

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;

$A_n = P( 1 + r)^n - M \times \left [ \dfrac{(1 + r)^n-1}{r} \right ]$

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;

$0 = 34006 \times \left ( 1 + \dfrac{0.091}{12} \right )^{84} - M \times \left [ \dfrac{\left (1 + \dfrac{0.091}{12} \right )^{84}-1}{\dfrac{0.091}{12} } \right ]$

$M = \dfrac{34006 \times \left ( 1 + \dfrac{0.091}{12} \right )^{84} }{\left [ \dfrac{\left (1 + \dfrac{0.091}{12} \right )^{84}-1}{\dfrac{0.091}{12} } \right ]} \approx 548.85$

Therefore, the approximate monthly payment = $548.85