After two years, a $1000 investment, compounded annually at interest rate r , will yield an amount of $1000 ( 1 + r ) ^ { 2 }$ . If the amount after two years is $1166.40, find the rate r . Round your answer to three decimal places.
A) $r = 2.080$
B) $r = 0.080$
C) $r = 0.166$
D) $r = 1.080$
E) $r = 1.166$

Question

Quizplus · Accepted Answer

We start by setting up the equation:

$$1000(1+r)^2 = 1166.40$$

Dividing both sides by 1000 gives:

$$(1+r)^2 = 1.1664$$

Taking the square root of both sides gives:

$$1+r = \sqrt{1.1664}$$

$$r = \sqrt{1.1664} - 1$$

Using a calculator, we find:

$$r \approx 0.080$$

Therefore, the answer is (B).

After Two Years, a $1000 Investment, Compounded Annually at Interest 1000(1+r)21000 ( 1 + r ) ^ { 2 }1000(1+r)2

After Two Years, a $1000 Investment, Compounded Annually at Interest $1000 ( 1 + r ) ^ { 2 }$