# If $2000 is invested at an interest rate of 4.5% per year, compounded continuously, find the value of the investment after the given number of years. (Round your answers to the nearest cent.) a) 2 years b) 4 years c) 12 years Question Decimals asked 2020-12-02 If$2000 is invested at an interest rate of 4.5% per year, compounded continuously, find the value of the investment after the given number of years. (Round your answers to the nearest cent.) a) 2 years b) 4 years c) 12 years 2020-12-03
Analyse the given information Since the interest is compounded continuously, the Principal will increase exponentially. The amount after t years is given by $$\displaystyle{A}{\left({t}\right)}={P}{e}^{{{r}{t}}}$$ It is given that the initial investment,$$\displaystyle{P}=\{2000}$$ and the interest rate per year,$$\displaystyle{r}={4.5}\%={0.045}$$ Process: In each part a), b) and c) plug in values of P, r and t in each case to find the value of Amount after a given number of years. To round to nearest cent we need to round answers to two decimals. a) After two years i.e t=2 $$\displaystyle{A}{\left({t}\right)}={P}{e}^{{{r}{t}}}$$ After two years: t=2 $$\displaystyle{A}{\left({2}\right)}={2000}{e}^{{{0.045}{\left({2}\right)}}}$$
$$\displaystyle{A}{\left({2}\right)}={2000}{e}^{{{0.09}}}$$
$$\displaystyle{A}{\left({2}\right)}=\{2188.35}$$ [rounded to two decimals(nearest cent) ] Amount after 2 years is $2188.35 b) After two years i.e t=4 $$\displaystyle{A}{\left({t}\right)}={P}{e}^{{{r}{t}}}$$ After two years: t=4 $$\displaystyle{A}{\left({4}\right)}={2000}{e}^{{{0.045}{\left({4}\right)}}}$$ $$\displaystyle{A}{\left({4}\right)}={2000}{e}^{{{0.18}}}$$ $$\displaystyle{A}{\left({4}\right)}=\{2394.43}$$ [rounded to two decimals(nearest cent) ] Amount after 4 years is$2394.43 c) After twelve years i.e t=12 $$\displaystyle{A}{\left({t}\right)}={P}{e}^{{{r}{t}}}$$ After two years: t=12 $$\displaystyle{A}{\left({12}\right)}={2000}{e}^{{{0.045}{\left({12}\right)}}}$$
$$\displaystyle{A}{\left({12}\right)}={2000}{e}^{{{0.54}}}$$
$$\displaystyle{A}{\left({12}\right)}=\{3432.01}$$ [rounded to two decimals(nearest cent)] Amount after 12 years is $3432.01 ### Relevant Questions asked 2020-11-08 Find the future value of an annuity of$ 1300 paid at the end of each year for 10 years, if interest is earned at a rate of $$7\%,$$ compounded annually. (Round your answer to the nearest cent.) A car has a purchase price of $24,800. The value declines continuously at an exponential rate of %23 annually. A. Wat is an equation modeling the value of this car after t years? B. What is its value after 6 years? c. How long will it take for its value to be$2000? 2. A bacteria colony grows continuously at an exponential rate. There are initially 1.1 million sent. After 5 days, there are 6.8 million present . a. What is the an equation modeling the number of bacteria present after d days? b. How many bacteria will be present after 7 days? c. How long will it take the number of bacteria to reach 92 million? Lance Jackson deposited $6,000 at Basil Bank at 8% interest compounded daily. What is Lance’s investment at the end of 4 years? (Use Table12.2.) (Do not round intermediate calculations. Round your answer to the nearest cent.) asked 2020-10-23 Find the present value of the ordinary annuity. If the amount of$500 of deposit in an account annually with an interest rate $$9\%$$ per year for 25 years. Solve for the value of x upto correct decimal approximation
$$\displaystyle{4400}={2000}{\left({1}+\frac{{{0.045}}}{{\left({12}\right)}^{{{12}{x}}}}\right.}$$
(solving this equation will determine the amount of time it takes an investment $2000 to grow$4400 if interest is 4.5% COMPOUNDED MONTHLY A random sample of $$\displaystyle{n}_{{1}}={16}$$ communities in western Kansas gave the following information for people under 25 years of age.
$$\displaystyle{X}_{{1}}:$$ Rate of hay fever per 1000 population for people under 25
$$\begin{array}{|c|c|} \hline 97 & 91 & 121 & 129 & 94 & 123 & 112 &93\\ \hline 125 & 95 & 125 & 117 & 97 & 122 & 127 & 88 \\ \hline \end{array}$$
A random sample of $$\displaystyle{n}_{{2}}={14}$$ regions in western Kansas gave the following information for people over 50 years old.
$$\displaystyle{X}_{{2}}:$$ Rate of hay fever per 1000 population for people over 50
$$\begin{array}{|c|c|} \hline 94 & 109 & 99 & 95 & 113 & 88 & 110\\ \hline 79 & 115 & 100 & 89 & 114 & 85 & 96\\ \hline \end{array}$$
(i) Use a calculator to calculate $$\displaystyle\overline{{x}}_{{1}},{s}_{{1}},\overline{{x}}_{{2}},{\quad\text{and}\quad}{s}_{{2}}.$$ (Round your answers to two decimal places.)
(ii) Assume that the hay fever rate in each age group has an approximately normal distribution. Do the data indicate that the age group over 50 has a lower rate of hay fever? Use $$\displaystyle\alpha={0.05}.$$
(a) What is the level of significance?
State the null and alternate hypotheses.
$$\displaystyle{H}_{{0}}:\mu_{{1}}=\mu_{{2}},{H}_{{1}}:\mu_{{1}}<\mu_{{2}}$$
$$\displaystyle{H}_{{0}}:\mu_{{1}}=\mu_{{2}},{H}_{{1}}:\mu_{{1}}>\mu_{{2}}$$
$$\displaystyle{H}_{{0}}:\mu_{{1}}=\mu_{{2}},{H}_{{1}}:\mu_{{1}}\ne\mu_{{2}}$$
$$\displaystyle{H}_{{0}}:\mu_{{1}}>\mu_{{2}},{H}_{{1}}:\mu_{{1}}=\mu_{{12}}$$
(b) What sampling distribution will you use? What assumptions are you making?
The standard normal. We assume that both population distributions are approximately normal with known standard deviations.
The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations,
The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations,
The Student's t. We assume that both population distributions are approximately normal with known standard deviations,
What is the value of the sample test statistic? (Test the difference $$\displaystyle\mu_{{1}}-\mu_{{2}}$$. Round your answer to three decimalplaces.)
What is the value of the sample test statistic? (Test the difference $$\displaystyle\mu_{{1}}-\mu_{{2}}$$. Round your answer to three decimal places.)
(c) Find (or estimate) the P-value.
P-value $$\displaystyle>{0.250}$$
$$\displaystyle{0.125}<{P}-\text{value}<{0},{250}$$
$$\displaystyle{0},{050}<{P}-\text{value}<{0},{125}$$
$$\displaystyle{0},{025}<{P}-\text{value}<{0},{050}$$
$$\displaystyle{0},{005}<{P}-\text{value}<{0},{025}$$
P-value $$\displaystyle<{0.005}$$
Sketch the sampling distribution and show the area corresponding to the P-value.
P.vaiue Pevgiue
P-value f P-value Suppose $10,000 is invested at an annual rate of $$\displaystyle{2.4}\%$$ for 10 years. Find the future value if interest is compounded as follows asked 2021-01-31 factor in determining the usefulness of an examination as a measure of demonstrated ability is the amount of spread that occurs in the grades. If the spread or variation of examination scores is very small, it usually means that the examination was either too hard or too easy. However, if the variance of scores is moderately large, then there is a definite difference in scores between "better," "average," and "poorer" students. A group of attorneys in a Midwest state has been given the task of making up this year's bar examination for the state. The examination has 500 total possible points, and from the history of past examinations, it is known that a standard deviation of around 60 points is desirable. Of course, too large or too small a standard deviation is not good. The attorneys want to test their examination to see how good it is. A preliminary version of the examination (with slight modifications to protect the integrity of the real examination) is given to a random sample of 20 newly graduated law students. Their scores give a sample standard deviation of 70 points. Using a 0.01 level of significance, test the claim that the population standard deviation for the new examination is 60 against the claim that the population standard deviation is different from 60. (a) What is the level of significance? State the null and alternate hypotheses. $$H_{0}:\sigma=60,\ H_{1}:\sigma\ <\ 60H_{0}:\sigma\ >\ 60,\ H_{1}:\sigma=60H_{0}:\sigma=60,\ H_{1}:\sigma\ >\ 60H_{0}:\sigma=60,\ H_{1}:\sigma\ \neq\ 60$$ (b) Find the value of the chi-square statistic for the sample. (Round your answer to two decimal places.) What are the degrees of freedom? What assumptions are you making about the original distribution? We assume a binomial population distribution.We assume a exponential population distribution. We assume a normal population distribution.We assume a uniform population distribution. asked 2020-11-26 The value of good wine increases with age. Thus, if you are a wine dealer, you have the problem of deciding whether to sell your wine now, at a price of$P a bottle, or to sell it later at a higher price. Suppose you know that the amount a wine-drinker is willing to pay for a bottle of this wine t years from now is \$P(1+20?t). Assuming continuous compounding and a prevailing interest rate of 5% per year, when is the best time to sell your wine? 