Question

Shawnee is putting $3,500 into an account earning 4.85% interest compounded quarterly. She estimates that it will take just over 11 years for this investment to grow to $6,000. Which of the following is a true statement?

a.
Shawnee’s estimate of the time is too low.
b.
Shawnee’s estimate of the time is correct.
c.
Shawnee’s estimate of the time is too high.
d.
Shawnee does not have enough information to estimate the time.

Answer 1

After applying the compound interest formula and solving for t, it's determined that it will take approximately 11.46 years for Shawnee's investment to grow to $6,000. Thus, Shawnee's estimate of just over 11 years is slightly too low.

The correct option is a.

Step-by-step explanation:

Shawnee's investment is governed by the formula for compound interest:

1. Determine the formula: A = P(1 + r/n)nt
2. Plug in the values: 6,000 = 3,500(1 + 0.0485/4)4t
3. Solve for t.

Let's solve the equation for t:

6,000 = 3,500(1 + 0.0485/4)4t

Divide both sides by 3,500:

1.714285714 = (1 + 0.012125)4t

Use logarithms to solve for t:

ln(1.714285714) = 4t * ln(1.012125)

t = [ln(1.714285714) / (4 * ln(1.012125))]

Calculate t:

t ≈ 11.46 years

Since Shawnee estimated it would take just over 11 years, her estimation is a bit too low; it will actually take approximately 11.46 years.