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Cerrena [4.2K]
2 years ago
9

Amber borrows $5,000 from the bank. If she repays the loan in 5 years, the annual interest rate is 8%, compounded annually. Howe

ver, if she can repay the loan in 3 years, the annual rate is 6.5%, compounded annually. How much interest will Amber save by repaying the loan in 3 years? (to the nearest dollar)
A) $1,152
B) $1,307
C) $583
D) $971
Mathematics
1 answer:
Svetllana [295]2 years ago
8 0

Answer:

The answer is (B) $1,307

Step-by-step explanation:

First you would plug the $5000, 5 Years and 8% Interest(Compound) into your Formula - A=P(1+r)t

A=5000(1+.08)5

Which the interest is $2346.64

<u>__      _________________________________________________</u>

Next you would plug $5000, 3 Years and 6.5% Interest(Compound) Into your Formula - A=P(1=r)t

A=5000(1+.065)3

Which the future value is $1039.75

<u>__       _________________________________________________</u>

Finally you would subtract $2346.64 by $1039.75 and then round the difference to the nearest dollar.      

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Answer:

Step-by-step explanation:

Hello!

The researcher developed a treatment to teach social skills to youth offenders. To test if the treatment is effective in increasing empathy compared to the standard treatment she randomly selected a group of 9 offenders and applied the new treatment and to another group of 9 randomly selected youth offenders, she applied the standard treatment. (Note: the data corresponds to two samples of 9 units each, so I've used those sizes to conduct the test)

At the end of the treatment, she administers BES to measure their empathy levels. Her claim is that the offenders that received the new treatment will have higher BES scores than those who received the standard treatment.

1) Using the records obtained for both groups, she  intends to conduct an independent t-test to analyze her claim.

X₁: BES results of a youth offender treated with the new treatment.

X₂: BES results of a youth offender treated with the standard treatment.

H₀: μ₁ = μ₂

H₁: μ₁ ≠ μ₂

α:0.05

test statistic

t_{H_0}= -0.32

p-value: 0.7517

The p-value is greater than the significance level so the decision is to not reject the null hypothesis. This means that at a 5% significance level you can conclude that there is no difference between the mean BES scores of the youth offenders treated with the new treatment and the mean BES score of  the youth offenders treated with the standard treatment. The new treatment doesn't increase the levels of social empathy of the youth offenders.

I hope this helps

(Box plot in attachment)

7 0
3 years ago
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