1 Answer

Rick Lancee · Answer 1 · 2019-10-24T08:26:53+0000

Answer: Cynthia must invest a smallest amount of 6911 pounds.

Step-by-step 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
$x_t= x\cdot 1.05^t$

Now we are looking at balance after t=3 years, and we know that balance should be 8000 pounds, or more.

$x\cdot 1.05^3 \geq 8000$

It is easy to solve for x:

$x \geq (8000)/(1.05^3)=(8000)/(1.1576)\approx6910.7$

So, for inequality to be satisfied, Cynthia must invest a smallest amount of 6911 pounds.

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