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

To determine Erica's approximate monthly payment on her student loans, we can use the formula for the sum of a finite geometric sequence. We can plug in the given values, such as the initial loan amount, the interest rate, and the number of years to pay off the loans, to calculate the monthly payment.

Step-by-step explanation:

To determine Erica's approximate monthly payment, we can use the formula for the sum of a finite geometric sequence. In this case, the sequence represents the monthly payments on Erica's student loans. The formula is given by:

P = A imes \frac{r(1 + r)^n}{(1 + r)^n - 1}

Where:

1. P is the monthly payment
2. A is the initial loan amount
3. r is the monthly interest rate
4. n is the total number of payments

Given that Erica has $34,006.00 in student loans, a fixed annual interest rate of 9.1%, and 7 years to pay off the loans, we can plug in these values into the formula:

P = 34006 imes \frac{0.091/12(1 + 0.091/12)^{7 imes 12}}{(1 + 0.091/12)^{7 imes 12} - 1}

Solving this equation will give us Erica's approximate monthly payment.