Answer:
I have to invest $11364.
Explanation:
The formula of Compound Interest is:

where A = Amount
P = Principle
r = rate
n = Number of Compounding per year
t = total number of year
Here, A = 15000, r = 5.75% = 0.0575, n = 4(quarterly), and t = 5.
Putting all these values in above formula:

⇒ 
⇒ 
⇒ 
⇒ P = 11364
Hence, I have to invest $11364 for 5 years.
We need the book to see what's happening
Answer:
a. Salary for the second year:
Salary is to increase by 4% in second year.
= 53,000 * (1 + 4%)
= $55,120
b. Third year salary:
Second year salary will increase by 5.5%
= 55,120 * (1 + 5.5%)
= $58,151.60
c. Fourth year salary:
Third year salary to increase by 11.1%
= 58,151.60 * (1 + 11.1%)
= $64,606.43