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Hmm if I'm not mistaken, is just an "ordinary" annuity, thus
![\bf \qquad \qquad \textit{Future Value of an ordinary annuity} \\\\ A=pymnt\left[ \cfrac{\left( 1+\frac{r}{n} \right)^{nt}-1}{\frac{r}{n}} \right] \\\\\\](https://tex.z-dn.net/?f=%5Cbf%20%5Cqquad%20%5Cqquad%20%5Ctextit%7BFuture%20Value%20of%20an%20ordinary%20annuity%7D%0A%5C%5C%5C%5C%0AA%3Dpymnt%5Cleft%5B%20%5Ccfrac%7B%5Cleft%28%201%2B%5Cfrac%7Br%7D%7Bn%7D%20%5Cright%29%5E%7Bnt%7D-1%7D%7B%5Cfrac%7Br%7D%7Bn%7D%7D%20%5Cright%5D%0A%5C%5C%5C%5C%5C%5C)
![\bf \begin{cases} A= \begin{array}{llll} \textit{original amount}\\ \textit{already compounded} \end{array} & \begin{array}{llll} \end{array}\\ pymnt=\textit{periodic payments}\to &400\\ r=rate\to 10\%\to \frac{10}{100}\to &0.1\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, so once} \end{array}\to &1\\ t=years\to &14 \end{cases} \\\\\\ A=400\left[ \cfrac{\left( 1+\frac{0.1}{1} \right)^{1\cdot 14}-1}{\frac{0.1}{1}} \right] ](https://tex.z-dn.net/?f=%5Cbf%20%5Cbegin%7Bcases%7D%0AA%3D%0A%5Cbegin%7Barray%7D%7Bllll%7D%0A%5Ctextit%7Boriginal%20amount%7D%5C%5C%0A%5Ctextit%7Balready%20compounded%7D%0A%5Cend%7Barray%7D%20%26%0A%5Cbegin%7Barray%7D%7Bllll%7D%0A%0A%5Cend%7Barray%7D%5C%5C%0Apymnt%3D%5Ctextit%7Bperiodic%20payments%7D%5Cto%20%26400%5C%5C%0Ar%3Drate%5Cto%2010%5C%25%5Cto%20%5Cfrac%7B10%7D%7B100%7D%5Cto%20%260.1%5C%5C%0An%3D%0A%5Cbegin%7Barray%7D%7Bllll%7D%0A%5Ctextit%7Btimes%20it%20compounds%20per%20year%7D%5C%5C%0A%5Ctextit%7Bannually%2C%20so%20once%7D%0A%5Cend%7Barray%7D%5Cto%20%261%5C%5C%0A%0At%3Dyears%5Cto%20%2614%0A%5Cend%7Bcases%7D%0A%5C%5C%5C%5C%5C%5C%0AA%3D400%5Cleft%5B%20%5Ccfrac%7B%5Cleft%28%201%2B%5Cfrac%7B0.1%7D%7B1%7D%20%5Cright%29%5E%7B1%5Ccdot%2014%7D-1%7D%7B%5Cfrac%7B0.1%7D%7B1%7D%7D%20%5Cright%5D%0A)
Answer:
1. y=1/4x+2
2. y=-3/2x +1
3. y = -3/2x -2
4. y= -3x -49
5. y = -2x +8
Step-by-step explanation:
1. Use slope intercept, y=mx+b where m =1/4 and b=2. y=1/4x+2
2. Use the point-slope form to write the equation, then simplify and convert into the slope intercept form.
(y-7)=-3/2(x--4)
y-7=-3/2(x+4)
y-7=-3/2x-6
y = -3/2x -6 +7
y=-3/2x +1
3. To write the equation of a line we must have a slope and a point. To find the slope we use the slope formula and substitute (x,y) points in it as shown below:
Now that we have the slope, plug in the slope and choose one point to plug into the point slope formula. Use the point-slope form to write the equation, then simplify and convert into the slope intercept form.
(y--5)=-3/2(x-2)
y+5=-3/2(x-2)
y+5=-3/2x + 3
y = -3/2x -2
4. Use the point-slope form to write the equation, then simplify and convert into the slope intercept form. The slope is -3 since parallel lines have the same slope.
(y--4)=-3(x-5)
y+4=-3 (x+15)
y+4=-3x -45
y= -3x -49
5. Use the point-slope form to write the equation, then simplify and convert into the slope intercept form. The slope is -2 since perpendicular lines have the negative reciprocal slopes. So 1/2 becomes -2.
(y--6)=-2(x-7)
y+6=-2 (x-7)
y+6 = -2x + 14
y = -2x +8