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1 year ago

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Colin invests £2350 into a savings account. The bank gives 4.2% compound interest for the first 4 years and 4.9% thereafter. How

much will Colin have after 10 years to the nearest pound?

1 answer:

MAXImum [283]1 year ago

3 0

Answer:

3691 pounds

Step-by-step explanation:

Given: Colin invests £2350 into a savings account. The bank gives 4.2% compound interest for the first 4 years and 4.9% thereafter

To find: Amount that Colin will have after 10 years

Solution:

Let P, r, n denotes principal, rate of interest and time period

For the first 4 years:

$P=\£\,2350\,,\,r=4.2\%\,,\,n=4$

Total amount after 4 years = $P\left ( 1+\frac{r}{100} \right )^n=2350\left ( 1+\frac{4.2}{100} \right )^4=\£ 2770.38$

For the next 6 years:

$P=\£\,2770.38\,,\,r=4.9\%\,,\,n=6$

Total amount after 6 years = $P\left ( 1+\frac{r}{100} \right )^n=2770.38\left ( 1+\frac{4.9}{100} \right )^6=3691.41\approx \£\,3691$

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Step-by-step explanation:

Data given and notation

$X_{1}=25$ represent the number of homeowners who would buy the security system

$X_{2}=9$ represent the number of renters who would buy the security system

$n_{1}=140$ sample 1

$n_{2}=60$ sample 2

$p_{1}=\frac{25}{140}=0.179$ represent the proportion of homeowners who would buy the security system

$p_{2}=\frac{9}{60}= 0.15$ represent the proportion of renters who would buy the security system

z would represent the statistic (variable of interest)

$p_v$ represent the value for the test (variable of interest)

Concepts and formulas to use

We need to conduct a hypothesis in order to check if the two proportions differs , the system of hypothesis would be:

Null hypothesis: $p_{1} = p_{2}$

Alternative hypothesis: $p_{1} \neq p_{2}$

We need to apply a z test to compare proportions, and the statistic is given by:

$z=\frac{p_{1}-p_{2}}{\sqrt{\hat p (1-\hat p)(\frac{1}{n_{1}}+\frac{1}{n_{2}})}}$ (1)

Where $\hat p=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{25+9}{140+60}=0.17$

Calculate the statistic

Replacing in formula (1) the values obtained we got this:

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