Calculate the accumulated amount after 3 years, if R5 000 is invested at an interest rate of 10% compounded quarterly?

2 answers:

7 0

$~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$5000\\ r=rate\to 10\%\to \frac{10}{100}\dotfill &0.10\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &3 \end{cases} \\\\\\ A=5000\left(1+\frac{0.10}{4}\right)^{4\cdot 3}\implies A=5000(1.025)^{12}\implies A\approx 6724.44$

timofeeve [1]2 years ago

3 0

Answer:

R6,724.44 or so I think that's right

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The mean family income for a random sample of 600 suburban households in Loganville shows that a 95 percent confidence interval

Misha Larkins [42]

Answer:

$43100 \leq \mu \leq 59710$

And for this case we want to test the following hypothesis:

Null hypothesis: $\mu =42000$

Alternative hypothesis: $\mu \neq 42000$

For this case since the lower value of the confidence interval is higher than 42000 we have enough evidence to reject the null hypothesis at the 55 of significance and we can conclude that the true mean is significantly different from 42000

Step-by-step explanation:

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)