A young couple purchases their first new home in 2002 for $120,000. They sell it to move into bigger home in 2007 for $150,000.

First, we will develop an exponential model for the value of the home. The model will have the form V(t)=V0ekt. Let t be years since 2002 and V(t) be the value of the home.

Mathematics

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Step-by-step explanation:

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Yolanda invests $30,000 in an account that offers a compound interest rate of 7.9% per year. Which of the following is the corre

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To find the solution, we will utilize the compound interest formula: $A=P(1+ \frac{r}{n} )^{nt}$
where
$A$ represents the total amount after $t$ years
tex]P[/tex] indicates the original investment
$r$ signifies the interest rate expressed in decimal
$n$ shows the frequency of compounding per year
$t$ indicates the duration in years

According to our problem, the initial investment is $30,000 with a duration of ten years, thus $P=30000$ and $t=10$ . Interest is compounded annually, so $n=1$ . To convert the percentage interest rate into decimal, we divide it by 100%
$r= \frac{7.9}{100}$
$r=0.079$
Now, we can insert these values into our formula:
$A=P(1+ \frac{r}{n} )^{nt}$
$A=30000(1+ \frac{0.079}{1} )^{(1)(10)}$
$A=3000(1+0.079)^{10}$
Substituting $A$ with $P_{10}$ :
$P_{10}=3000(1+0.079)^{10}$

Consequently, we find that the correct answer is D. $P_{10}=3000(1+0.079)^{10}$

Finally, to determine the total amount Yolanda will have after ten years, we just need to carry out the operations in our equation:
 $P_{10}=3000(1+0.079)^{10}$
$P_{10}=30000(1.079)^{10}$
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Thus, we conclude that Yolanda will end up with $64,170.54 in her account after a decade of earning at a compound interest rate of 7.9% yearly.

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