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ZanzabumX [31]
3 years ago
10

Brian invests $10,000 in an account earning 4% interest, compounded annually for 10 years. Five years after Brian's initial inve

stment, Chris invests $10,000 in an account earning 7% interest, compounded annually for 5 years. Given that no additional deposits are made, compare the balances of the two accounts after the interest period ends for each account. (round to the nearest dollar) A) Chris has $766 more in his account than Brian. B) Brian has $766 more in his account than Chris. C) Chris has $1,593 more in his account than Brian. D) Brian has $1,593 more in his account than Chris.
Mathematics
1 answer:
pentagon [3]3 years ago
6 0

Answer:

Brian has $776 more account in his account than Chris.

Step-by-step explanation:

Compound interest Formula:

A=P(1+r)^t

I= A-P

A= Amount after t years

P= Initial amount

r= Rate of interest

t= Time in year

Given that,

Brian invests $10,000 in an account earning 4% interest, compounded annually for 10 years.

Here P = $10,000 , r= 4%=0.04, t=10 years

The amount in his account after 10 years is

A=10000(1+0.04)^{10}

   =$14802.44

  ≈$14802

Five years after Brian's investment,Chris invests $10,000 in an account earning 7% interest, compounded annually for 5 years.

Here P = $10,000 , r= 7%=0.07, t=5 years

The amount in his account after 5 years is

A=10000(1+0.07)^{5}

   =$14025.51

  ≈$14026

From the it is cleared that Brian has $(14802-14026)=$776 more account in his account than Chris.

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3 years ago
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<h3>Answer:  50</h3>

==========================================================

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In a random sample of 400 residents of Boston, 320 residents indicated that they voted for Obama in the last presidential electi
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C.I =  0.7608   ≤ p ≤   0.8392

Step-by-step explanation:

Given that:

Let consider a  random sample n = 400 candidates where  320 residents indicated that they voted for Obama

probability \hat p = \dfrac{320}{400}

= 0.8

Level of significance ∝ = 100 -95%

= 5%

= 0.05

The objective is to  develop a 95% confidence interval estimate for the proportion of all Boston residents who voted for Obama.

The confidence internal can be computed as:

=\hat p  \pm Z_{\alpha/2} \sqrt{\dfrac{ p(1-p)}{n } }

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SO;

=0.8  \pm 1.960 \sqrt{\dfrac{ 0.8(1-0.8)}{400 } }

=0.8  \pm 1.960 \sqrt{\dfrac{ 0.8(0.2)}{400 } }

=0.8  \pm 1.960 \sqrt{\dfrac{ 0.16}{400 } }

=0.8  \pm 1.960 \sqrt{4 \times 10^{-4}}

=0.8  \pm 1.960 \times 0.02}

=0.8  \pm 0.0392

= 0.8 - 0.0392     OR   0.8 + 0.0392  

= 0.7608    OR    0.8392

Thus; C.I =  0.7608   ≤ p ≤   0.8392

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3 years ago
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