Question

Leila deposited $6000 into an account with a 4.3% annual interest rate, compounded quarterly. Assuming that no withdrawals are made, how long will it take for the investment to grow to $7500? Do not round any intermediate computations, and round your answer to the nearest hundredth.

If necessary, refer to the list of financial formulas.
years

Answer 1

To determine how long it will take for the investment to grow to $7500, we can use the formula for compound interest. After substituting the given values into the formula and solving for t, we find that it will take approximately 3.76 years for the investment to reach $7500.

Step-by-step explanation:

To determine how long it will take for the investment to grow to $7500, we can use the formula for compound interest:

Substitute the given values into the formula:A = P(1 + r/n)^(nt)A = 7500, P = 6000, r = 4.3%, n = 4 (quarterly),Solve for t:

7500 = 6000(1 + 0.043/4)^(4t)

Divide both sides of the equation by 6000:

7500/6000 = (1 + 0.043/4)^(4t)

1.25 = (1 + 0.01075)^4t

Take the natural logarithm of both sides:

ln(1.25) ≈ 4t × ln(1.01075)

Divide both sides by 4 × ln(1.01075):

t ≈ ln(1.25) / (4 × ln(1.01075))

Using a calculator, we find that:

t ≈ 3.76

Therefore, it will take approximately 3.76 years for the investment to grow to $7500.