Many couples believe that it is getting too expensive to host an "average" wedding in the United States. According to the websit
1 answer:
Answer:
Step-by-step explanation:
Given that many couples believe that it is getting too expensive to host an "average" wedding in the United States.
Population mean =24066
Sample mean = 23224
Sample size = 40
Sample std dev = 2903
Since sample std dev is known, we use t critical value.
df =39
Sample mean follows a normal distribution with mean = 23224, and std dev =
t critical value = 2.023
Margin of error = 2.023*459.005
Confidence interval
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how much will it be in 16 years?
![\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)
![\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 &40,000\\ r=rate\to 3\%\to \frac{3}{100}\to &0.03\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\to &1\\ t=years\to &16 \end{cases} \\\\\\ A=40000\left[ \cfrac{\left( 1+\frac{0.03}{1} \right)^{1\cdot 16}-1}{\frac{0.03}{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%0A%5Cbegin%7Barray%7D%7Bllll%7D%0A%0A%5Cend%7Barray%7D%5C%5C%0Apymnt%3D%5Ctextit%7Bperiodic%20payments%7D%5Cto%20%2640%2C000%5C%5C%0Ar%3Drate%5Cto%203%5C%25%5Cto%20%5Cfrac%7B3%7D%7B100%7D%5Cto%20%260.03%5C%5C%0An%3D%0A%5Cbegin%7Barray%7D%7Bllll%7D%0A%5Ctextit%7Btimes%20it%20compounds%20per%20year%7D%5C%5C%0A%5Ctextit%7Bannually%2C%20thus%20once%7D%0A%5Cend%7Barray%7D%5Cto%20%261%5C%5C%0A%0At%3Dyears%5Cto%20%2616%0A%5Cend%7Bcases%7D%0A%5C%5C%5C%5C%5C%5C%0AA%3D40000%5Cleft%5B%20%5Ccfrac%7B%5Cleft%28%201%2B%5Cfrac%7B0.03%7D%7B1%7D%20%5Cright%29%5E%7B1%5Ccdot%20%2016%7D-1%7D%7B%5Cfrac%7B0.03%7D%7B1%7D%7D%20%5Cright%5D)
how much will it be in 16 years?