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

Question

Zinaida

3 months ago

15

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

ct equation for how much Yolanda will have after 10 years?
Possible answers here: https://imgur.com/M5JkywQ

Mathematics

1 answer:

Zina [12.3K] · Answer 1 · 2026-02-23T16:25:36+03:00

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:
 $P_{10}=3000(1+0.079)^{10}$
$P_{10}=30000(1.079)^{10}$
$P_{10}=64170.54$

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.