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 ]](https://tex.z-dn.net/?f=A_n%20%3D%20P%28%201%20%2B%20r%29%5En%20-%20M%20%5Ctimes%20%5Cleft%20%5B%20%5Cdfrac%7B%281%20%2B%20r%29%5En-1%7D%7Br%7D%20%5Cright%20%5D)
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 ]](https://tex.z-dn.net/?f=0%20%3D%2034006%20%5Ctimes%20%5Cleft%20%28%201%20%2B%20%5Cdfrac%7B0.091%7D%7B12%7D%20%5Cright%20%29%5E%7B84%7D%20-%20M%20%5Ctimes%20%5Cleft%20%5B%20%5Cdfrac%7B%5Cleft%20%281%20%2B%20%5Cdfrac%7B0.091%7D%7B12%7D%20%5Cright%20%29%5E%7B84%7D-1%7D%7B%5Cdfrac%7B0.091%7D%7B12%7D%20%7D%20%5Cright%20%5D)
![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](https://tex.z-dn.net/?f=M%20%3D%20%5Cdfrac%7B34006%20%5Ctimes%20%5Cleft%20%28%201%20%2B%20%5Cdfrac%7B0.091%7D%7B12%7D%20%5Cright%20%29%5E%7B84%7D%20%20%7D%7B%5Cleft%20%5B%20%5Cdfrac%7B%5Cleft%20%281%20%2B%20%5Cdfrac%7B0.091%7D%7B12%7D%20%5Cright%20%29%5E%7B84%7D-1%7D%7B%5Cdfrac%7B0.091%7D%7B12%7D%20%7D%20%5Cright%20%5D%7D%20%5Capprox%20548.85)
Therefore, the approximate monthly payment = $548.85
Treat each (time, money) pair as an (x, y) pair, and get the slope of the line:
For Rosita, (5, 128), (7, 164): m = (y2 - y1)/(x2 - x1) = (164 - 128)/(7 - 5) = 18, implying that she earns $18/hr. The y-intercept is calculated as: y = 18x + b, 128 = 18*5 + b, b = $38, meaning that she started with $38. Rosita's equation is y = 18x + 38.
For Garth, (3, 124), (8, 194): m = (194 - 124)/(8 - 3) = 14. For 124 = 14*3 + b, b = $82. Garth's equation is y = 14x + 82
To find out when they will have saved the same amount, both equations would have the same y-value:
18x + 38 = 14x + 82
4x = 44
x = 11 hours
y = 18*11 + 38 = $236 (alternatively, y = 14*11 + 82 = 236)
This means that Rosita and Garth will have both saved $236 after 11 hours of working.
Answer:
let number of mile on monday be x
tuesday = 9/10 of x
wednesday = 9/20 of x
Step-by-step explanation:
tues = 90/100=9/10
wednes = 50/100 * 90/100 * x
wednes = 9/20 of x
Answer: PG = 1/3JG = 1/3 x 18 = 18/3 = 6
