1. -3/2
2. 2
3. 1/2
4.0
5. 1/2
6. -3/4
7. -1/4
8. -8/11
9. 0
10. -1/5
Answer:
Amount = $11025
Interest = $1025
Step-by-step explanation:
Amount in a compound interest is given by
![A = P\left(1+\dfrac{R}{100}\right)^T](https://tex.z-dn.net/?f=A%20%3D%20P%5Cleft%281%2B%5Cdfrac%7BR%7D%7B100%7D%5Cright%29%5ET)
where P is the principal, R is the rate and T is the time.
The interest is compunded quarterly i.e. 4 times a year. Hence its rate per quarter will be 20% ÷ 4 = 5%.
The principal is compunded for six months which is 2 quarters. Therefore, T = 2.
![A = 10000(1+\frac{5}{100})^2 = 10000(1.05)^2 = 11025](https://tex.z-dn.net/?f=A%20%3D%2010000%281%2B%5Cfrac%7B5%7D%7B100%7D%29%5E2%20%3D%2010000%281.05%29%5E2%20%3D%2011025)
The interest is A - P = 11025 - 10000 = $1025
Gg71.555 us nsmsvs slonbg perthebs
![\text{Let the man drove 13 miles directly east from home, A and reach an}\\ \text{intersection point B. Then take a left turn and traveled 5 miles due north}\\ \text{to reach his place of work C.}\\ \\ \text{now if a road was made directly from his home to his place of work,}\\ \text{the distance AC can be found using the Pythagorean theorem. so we have}](https://tex.z-dn.net/?f=%5Ctext%7BLet%20the%20man%20drove%2013%20miles%20%20directly%20east%20from%20home%2C%20A%20and%20reach%20an%7D%5C%5C%0A%5Ctext%7Bintersection%20point%20B.%20Then%20take%20a%20left%20turn%20and%20traveled%205%20miles%20due%20north%7D%5C%5C%0A%5Ctext%7Bto%20reach%20his%20place%20of%20work%20C.%7D%5C%5C%0A%5C%5C%0A%5Ctext%7Bnow%20if%20a%20road%20was%20made%20directly%20from%20his%20home%20to%20his%20place%20of%20work%2C%7D%5C%5C%0A%5Ctext%7Bthe%20distance%20AC%20can%20be%20found%20using%20the%20Pythagorean%20theorem.%20so%20we%20have%7D)
![(AC)^2=(AB)^2+(BC)^2\\ \\ \Rightarrow (AC)^2=(13)^2+(5)^2\\ \\ \Rightarrow (AC)^2=169+25\\ \\ \Rightarrow (AC)^2=194\\ \\ \Rightarrow AC=\sqrt{194}\\ \\ \Rightarrow AC \approx 13.93](https://tex.z-dn.net/?f=%28AC%29%5E2%3D%28AB%29%5E2%2B%28BC%29%5E2%5C%5C%0A%5C%5C%0A%5CRightarrow%20%28AC%29%5E2%3D%2813%29%5E2%2B%285%29%5E2%5C%5C%0A%5C%5C%0A%5CRightarrow%20%28AC%29%5E2%3D169%2B25%5C%5C%0A%5C%5C%0A%5CRightarrow%20%28AC%29%5E2%3D194%5C%5C%0A%5C%5C%0A%5CRightarrow%20AC%3D%5Csqrt%7B194%7D%5C%5C%0A%5C%5C%0A%5CRightarrow%20AC%20%5Capprox%2013.93)
Hence the distance from his home to work place is approximately 13.93 miles