Question

Find out how long it takes a $2,700 investment to double if it is invested at 9% compounded semiannually. Round to the nearest tenth of a year. Use the formula A = A = P(1 + r/n)^(nt).

a) 8.3 years
b) 7.9 years
c) 8.1 years
d) 7.7 years

Answer 1

To find out how long it takes a $2,700 investment to double at 9% compounded semiannually, you can use the formula for compound interest. Using the formula A = P(1 + r/n)^(nt) and solving for t, you will find that it takes approximately 8.1 years for the investment to double.

Step-by-step explanation:

To find out how long it takes a $2,700 investment to double at 9% compounded semiannually, we can use the formula for compound interest:

A = P(1 + r/n)^(nt).

In this case, P = $2,700, r = 9%, n = 2 (since it's compounded semiannually), and we need to solve for t.

We want to find the value of t when A = 2P (since we want the investment to double). So the equation becomes

2,700(1 + 0.09/2)^(2t) = 2 * 2,700. Solving for t:

2.045^t = 2

t ≈ 8.1 years