Question

Amanda invests $6,062 in a savings account with a fixed annual interest rate of 4 % compounded 12 times per year. How long will it take for the account balance to reach $7,401.68?

Answer 1

To calculate how long it will take for the account balance to reach $7,401.68 in a savings account with a fixed annual interest rate of 4% compounded 12 times per year, we can use the formula for compound interest. Substituting the given values and simplifying the equation, we find that it will take approximately 10.67 years for the account balance to reach $7,401.68.

Step-by-step explanation:

To calculate how long it will take for the account balance to reach $7,401.68, we can use the formula for compound interest:

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

Where A is the future value, P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.

1. Substituting the given values into the formula, we have: $7401.68 = $6062(1 + 0.04/12)^(12t)
2. Now we can simplify the equation:
3. 0.403 = (1.0033333333333333)^(12t)
4. Take the natural log of both sides:
5. ln(0.403) = ln((1.0033333333333333)^(12t))
6. Using the logarithmic properties, we get:
7. t = ln(0.403) / (12ln(1.0033333333333333))
8. Calculating the value of t gives us:
9. t ≈ 10.67 years

Therefore, it will take approximately 10.67 years for the account balance to reach $7,401.68.