Question

Suppose $6700 is invested in a savings account for 10 years (120 Months), with an annual interest rate of r, compounded monthly. The amount of money in the account after ten years is:

A(r) = 6700(1+r/12)¹²⁰
What is the Approximate interest rate needed to reach $7000 over 10 years? Here is what I have:
7000 = 6700(1+r/12)¹²⁰
HOW DO YOU MANIPULATE the equation?

Answer 1

The approximate annual interest rate needed to reach $7000 over 10 years is 0.54%.

To approximate the interest rate needed to reach $7000 over 10 years, we can follow these steps:

1. Isolate the term with the interest rate: Divide both sides of the equation by 6700:

1.045 = (1+r/12)^120

2. Simplify the equation: Take the 120th root of both sides:

1.00375 = 1+r/12

3. **Solve for r:** Subtract 1 from both sides and multiply both sides by 12:

r = 0.00375 * 12 ≈ 0.045%

4. **Convert to annual interest rate:** Since the interest is compounded monthly, we need to multiply the monthly rate by 12 to get the annual rate:

0.045% * 12 ≈ 0.54%