Answer:
Given that,
An amount of $23,000 is borrowed for 11 years at 6.75% interest, compounded annually.
To find the Amount paid back after 11 years.
Step-by-step explanation:
we know that,
The formula to find the,
Amount after n years of interest rate r% compounded annually is,
![A=P(1+(r)/(100))^n](https://img.qammunity.org/2023/formulas/mathematics/high-school/sg4zk7ybldcrek0y9wnq377cpzs7p93hjn.png)
where P is the initial amount.
Here, we have that,
P=$23,000
r=6.75
n=11
Substitute the values we get,
![A=23000(1+(6.75)/(100))^(11)](https://img.qammunity.org/2023/formulas/mathematics/college/jbvszsqvusf17vk2j9dc0zaq3vz5zq8uug.png)
Solving this we get,
![A=23000(1+0.0675)^(11)](https://img.qammunity.org/2023/formulas/mathematics/college/nics077vw1gfqbp4yjgb9ogh5gnqmz99dg.png)
![A=23000(1.0675)^(11)](https://img.qammunity.org/2023/formulas/mathematics/college/gy7uzct2q5i28ng7u6zlijpd2bmp5hhsnw.png)
![A=23000(2.05138)](https://img.qammunity.org/2023/formulas/mathematics/college/sghem7q67a3w5lcnjjw6sp31wfnulessc1.png)
![A=47181.805](https://img.qammunity.org/2023/formulas/mathematics/college/9lep4rd72ner9hw2js1npakersgy9cy34s.png)
Round to the nearest dollar.
![A=47181.805\approx47182](https://img.qammunity.org/2023/formulas/mathematics/college/v2ja6rpiudg1t2l0mgwt3y4lyovxni28ev.png)
Answer is: Amount paid back is $47182 after 11 years