Answer: Cynthia must invest a smallest amount of 6911 pounds.
Explanation:
Compound interest makes the initial deposit grow exponentially in the number of years. So let us denote the initial investment (deposit) x.
After one year the balance with interest will be x(1+0.05)=x*1.05
After two years the balance will be (x*1.05)*1.05, and so on.
After t years the balance will be
Now we are looking at balance after t=3 years, and we know that balance should be 8000 pounds, or more.
It is easy to solve for x:
So, for inequality to be satisfied, Cynthia must invest a smallest amount of 6911 pounds.