For 3 years, regular weekly payments of 50 are deposited into an account that compounds interest weekly.If the final value of the account is 8600, what was the interest rate? Select one: a. 6.43% b. 6.51% C. 6.45% d. 6.23%

Here's how to solve this problem:<br /><br />**1. Determine the total number of payments:**<br /><br />* There are 52 weeks in a year.<br />* Over 3 years, there are 3 * 52 = 156 weekly payments.<br /><br />**2. Use the future value of an ordinary annuity formula:**<br /><br />The future value (FV) of an ordinary annuity is given by:<br /><br />FV = P * [((1 + r)^n - 1) / r]<br /><br />Where:<br /><br />* FV = Future Value ($8600)<br />* P = Periodic Payment ($50)<br />* r = Interest rate per period (weekly rate, which we need to find)<br />* n = Number of periods (156)<br /><br />**3. Solve for 'r':**<br /><br />$8600 = 50 * [((1 + r)^156 - 1) / r]$<br /><br />This equation is difficult to solve algebraically. We'll use an iterative approach or a financial calculator.<br /><br />**Iterative Approach (Trial and Error):**<br /><br />We can test the given answer choices to see which one gets us closest to $8600. Remember to convert the annual interest rate to a weekly rate by dividing by 52.<br /><br />* **a. 6.43%:** Weekly rate = 0.0643 / 52 = 0.0012365. FV = $50 * [((1 + 0.0012365)^156 - 1) / 0.0012365] ≈ $8586.81<br />* **b. 6.51%:** Weekly rate = 0.0651 / 52 = 0.0012519. FV = $50 * [((1 + 0.0012519)^156 - 1) / 0.0012519] ≈ $8613.55<br />* **c. 6.45%:** Weekly rate = 0.0645 / 52 = 0.0012404. FV = $50 * [((1 + 0.0012404)^156 - 1) / 0.0012404] ≈ $8593.66<br />* **d. 6.23%:** Weekly rate = 0.0623/52 = 0.0011981. FV = $50 * [((1 + 0.0011981)^156 - 1) / 0.0011981] ≈ $8533.12<br /><br />**4. Choose the closest answer:**<br /><br />The closest answer is **b. 6.51%**, as it results in a future value of approximately $8613.55, which is very close to the target of $8600.<br /><br />**Therefore, the answer is b.**<br />