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stellarik [79]
3 years ago
6

Karen Gaines invested $12,000 in a money market account with an interest rate of 2.25% compounded semiannually. Six years later,

Karen withdrew the full amount to put toward the down payment
on a new house. How much did Karen withdraw from the account?

(Round to the nearest cent as needed.)
Mathematics
2 answers:
deff fn [24]3 years ago
8 0

Answer:

$13,724

Step-by-step explanation:

From the above question, we are given the following values:

Principal = P = $12,000

Interest = r = 2.25% = 0.0225

Compounded semi annually = n = 2

Time (t) = 6 years

From the question, we understand that we are to find the total (full) Amount Karen withdrew.

The formula to use to calculate the Total Amount of money given that this is a compound interest question is:

Total(full) Amount = P( 1 + r/n) ^n/t

= $12,000( 1 + 0.0225/2) ^2×6

= $12,000(1.01125)^12

= $13724.093289

Approximately to the nearest cent

≈ $13,724

Therefore, Karen withdrew $13,724 from the account.

Alex3 years ago
4 0

Karen Gaines invested $14000 in a money market account with an interest rate of 2.75% compounded semiannually. Six years later, Karen withdrew the full amount to put toward the down payment

Round to the nearest cent as needed.)

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3 years ago
Malco weighs 42 more pounds than Peter the sum of their Weights is 286 pounds how much does Peter way
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How can i prove this property to be true for all values of n, using mathematical induction.
chubhunter [2.5K]

Proof -

So, in the first part we'll verify by taking n = 1.

\implies \: 1  =  {1}^{2}  =  \frac{1(1 + 1)(2 + 1)}{6}

\implies{ \frac{1(2)(3)}{6} }

\implies{ 1}

Therefore, it is true for the first part.

In the second part we will assume that,

\: {  {1}^{2} +  {2}^{2}  +  {3}^{2}  + ..... +  {k}^{2}  =  \frac{k(k + 1)(2k + 1)}{6}  }

and we will prove that,

\sf{ \: { {1}^{2} +  {2}^{2}  +  {3}^{2}  + ..... +  {k}^{2}  + (k + 1)^{2} =  \frac{(k + 1)(k + 1 + 1) \{2(k + 1) + 1\}}{6}}}

\: {{1}^{2} +  {2}^{2}  +  {3}^{2}  + ..... +  {k}^{2}  + (k + 1)^{2}  =  \frac{(k + 1)(k + 2) (2k + 3)}{6}}

{1}^{2} +  {2}^{2}  +  {3}^{2}  + ..... +  {k}^{2}  + (k + 1)^{2} = \frac{k (k + 1) (2k + 1) }{6} +  \frac{(k + 1) ^{2} }{6}

{1}^{2} +  {2}^{2}  +  {3}^{2}  + ..... +  {k}^{2}  + (k + 1)^{2} = \frac{k(k+1)(2k+1)+6(k+1)^ 2 }{6}

{1}^{2} +  {2}^{2}  +  {3}^{2}  + ..... +  {k}^{2}  + (k + 1)^{2} = \frac{(k+1)\{k(2k+1)+6(k+1)\} }{6}

{1}^{2} +  {2}^{2}  +  {3}^{2}  + ..... +  {k}^{2}  + (k + 1)^{2} = \frac{(k+1)(2k^2 +k+6k+6) }{6}

{1}^{2} +  {2}^{2}  +  {3}^{2}  + ..... +  {k}^{2}  + (k + 1)^{2} = \frac{(k+1)(2k^2+7k+6) }{6}

{1}^{2} +  {2}^{2}  +  {3}^{2}  + ..... +  {k}^{2}  + (k + 1)^{2} = \frac{(k+1)(k+2)(2k+3) }{6}

<u>Henceforth, by </u><u>using </u><u>the </u><u>principle </u><u>of </u><u> mathematical induction 1²+2² +3²+....+n² = n(n+1)(2n+1)/ 6 for all positive integers n</u>.

_______________________________

<em>Please scroll left - right to view the full solution.</em>

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<h3>Graph of inequalities</h3>

Inequalities are expression not separated by an equal sign. According to the question, we ned the inequality's graph that will have a dashed boundary line.

An inequality that will have solid boundary line must include only the less than or equal to sign < or greater than or equal to > sign.

From the option given, none of the inequality is correct since there is absence of equal sign.

Learn more on inequality graph here: brainly.com/question/24372553

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