![\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)
![\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 & \begin{array}{llll} 485\cdot 12\\ \underline{5280} \end{array}\\ r=rate\to 6\%\to \frac{6}{100}\to &0.06\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{a year, thus once} \end{array}\to &1\\ t=years\to &4 \end{cases} \\\\\\ ](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%26%0A%5Cbegin%7Barray%7D%7Bllll%7D%0A485%5Ccdot%2012%5C%5C%0A%5Cunderline%7B5280%7D%0A%5Cend%7Barray%7D%5C%5C%0Ar%3Drate%5Cto%206%5C%25%5Cto%20%5Cfrac%7B6%7D%7B100%7D%5Cto%20%260.06%5C%5C%0An%3D%0A%5Cbegin%7Barray%7D%7Bllll%7D%0A%5Ctextit%7Btimes%20it%20compounds%20per%20year%7D%5C%5C%0A%5Ctextit%7Ba%20year%2C%20thus%20once%7D%0A%5Cend%7Barray%7D%5Cto%20%261%5C%5C%0A%0At%3Dyears%5Cto%20%264%0A%5Cend%7Bcases%7D%0A%5C%5C%5C%5C%5C%5C%0A)
![\bf A=5280\left[ \cfrac{\left( 1+\frac{0.06}{1} \right)^{1\cdot 4}-1}{\frac{0.06}{1}} \right]](https://tex.z-dn.net/?f=%5Cbf%20A%3D5280%5Cleft%5B%20%5Ccfrac%7B%5Cleft%28%201%2B%5Cfrac%7B0.06%7D%7B1%7D%20%5Cright%29%5E%7B1%5Ccdot%20%204%7D-1%7D%7B%5Cfrac%7B0.06%7D%7B1%7D%7D%20%5Cright%5D)
Joe is making $485 payments monthly, but the amount gets interest on a yearly basis, not monthly, so the amount that yields interest is 485*12
also, keep in mind, we're assuming is compound interest, as opposed to simple interest
Ok, so.
You first need to find the height of the shorts guy's setup. We know that the length of the base is 14.5, and that theta is 46 degrees. The opposite side equals tan46 * 14.5, which is 14.935. 14.935 is the height of the short guy's height. Now onto the other dude. We know that the height of his setup is 4.2 more than the shorts guy, which is equal to 19.13. Finally, to find the angle, theta, of the second guy, we take 19.13 / 14.5 and then take the inverse tangent of that number (1.31) which equals approximately 52.6 degrees.
Answer:
It takes Carrie and James an hour and a half to finish the job.
Step-by-step explanation:
assuming they have to inspect ONE case of watches.
Carrie can inspect 1/5 case in one hour.
James can inspect 1/3 case in one hour.
Carrie worked alone for 1 hour, so she finished 1/5 of a case.
She leaves 4/5 case to finish.
She had lunch.
After that, Carrie and James worked together for x hours to finish the job.
When they work together, the finish 1/5+1/3 = 8/15 case per hour.
So time to finisher the remaining case
Time = 4/5 / (8/15)
= 4/5 * 15/8
= 3/2 hours
= an hour and a half.
Adjusted balance
$400.00 - ($35.85 + $10.42) + $120.00 = $473.73