Question

anna is going in a 2-year medial assistant trade school. she has been awarded a $8,100 subsidized federal loan for both years at 5.50%
what will be her monthly payemnt for the next 10 years?
m=p(r/12)(1+r/12)^12(t)/((1+r/12)^12(t)-1)
$312.05
$87.91
$124.12
$168.91

Explanation:

Step1: Define variables

Let $P = 8100$, $r = 0.055$, $t = 10$

Step2: Calculate monthly rate & total periods

Monthly rate: $\frac{r}{12} = \frac{0.055}{12} \approx 0.004583$; Total periods: $12t = 120$

Step3: Compute compound factor

$(1+\frac{r}{12})^{12t} = (1+\frac{0.055}{12})^{120} \approx 1.73107$

Step4: Apply loan payment formula

$M = P \cdot \frac{\frac{r}{12}(1+\frac{r}{12})^{12t}}{(1+\frac{r}{12})^{12t}-1}$
Substitute values:
$M = 8100 \cdot \frac{0.004583 \times 1.73107}{1.73107-1}$

Step5: Simplify to find payment

First calculate numerator: $0.004583 \times 1.73107 \approx 0.007934$
Denominator: $1.73107-1 = 0.73107$
$M = 8100 \times \frac{0.007934}{0.73107} \approx 8100 \times 0.01085 \approx 87.91$

Answer:

$87.91$ (the second option)