Question

julia just graduated from college and owes $12,100 on her student loans. the bank charges a monthly interest rate of 0.225%. if julia wants to pay off her student loans using equal monthly payments over the next 11 years, what would the monthly payment be, to the nearest dollar?

m = \frac{pr(1 + r)^n}{(1 + r)^n - 1}

$m =$ the monthly payment
$p =$ the amount owed
$r =$ the interest rate per month
$n =$ the number of payments

Explanation:

Step1: Identify the values

$P = 12100$, $r=0.00225$, $n = 11\times12=132$

Step2: Substitute into the formula

$M=\frac{12100\times0.00225\times(1 + 0.00225)^{132}}{(1 + 0.00225)^{132}-1}$
First, calculate $(1 + 0.00225)^{132}$. Let $x=(1 + 0.00225)^{132}$. Using the formula for compound - interest $(a + b)^n=\sum_{k = 0}^{n}\binom{n}{k}a^{n - k}b^{k}$, or simply using a calculator, $x\approx1.3477$.
Then, $12100\times0.00225 = 27.225$.
The numerator is $27.225\times1.3477\approx36.69$.
The denominator is $1.3477-1 = 0.3477$.
$M=\frac{36.69}{0.3477}\approx106$.

Answer:

$106$