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Question 2Suppose a principal of $500 is placed in a bank account paying interest of 6% p.a. compoundedweekly. If no money is withdrawn from the account, how long (in weeks) will it take for theaccount balance to reach $700?Note: round your answer to the nearest whole number.

Question

Question 2Suppose a principal of 500isplacedinabankaccountpayinginterestof6500 is placed in a bank account paying interest of 6% p.a. compoundedweekly. If no money is withdrawn from the account, how long (in weeks) will it take for theaccount balance to reach 700?Note: round your answer to the nearest whole number.

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Solution

Sorry, there seems to be a misunderstanding. I believe you want me to solve the problem. Here's how to do it:

Step 1: Understand the problem We are given that the principal (P) is 500,theinterestrate(r)is6500, the interest rate (r) is 6% per annum compounded weekly, and the final amount (A) is 700. We need to find the time (t) in weeks.

Step 2: Convert the interest rate Since the interest is compounded weekly, we need to convert the annual interest rate to a weekly interest rate. There are approximately 52 weeks in a year, so the weekly interest rate is 6% / 52 = 0.11538%.

Step 3: Use the compound interest formula The formula for compound interest is A = P(1 + r/n)^(nt), where:

  • A is the amount of money accumulated after n years, including interest.
  • P is the principal amount (the initial amount of money)
  • r is the annual interest rate (in decimal)
  • n is the number of times that interest is compounded per year
  • t is the time the money is invested for in years

In this case, we need to rearrange the formula to solve for t: t = log(A/P) / (n * log(1 + r/n))

Step 4: Substitute the values into the formula t = log(700/500) / (52 * log(1 + 0.0011538))

Step 5: Solve for t Using a calculator, we find that t ≈ 82.3 weeks.

So, it will take approximately 82 weeks for the account balance to reach $700.

This problem has been solved

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