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Clearwater State Bank is offering an introductory 20% interest rate on a new account, which will compound semi-annually for the first two years, then compound 5% annually thereafter. Customer 1 deposits $100 in that account to start. To compete, Clearwater Credit Union is offering a similar offer. Their newest account offers an introductory rate of 15% compounded quarterly for the first year, and a rate of 6% compounded quarterly thereafter. Customer 2 deposits an unknown amount with Clearwater Credit Union. After two years, the customers had an equal amount saved.
Q. From the choices below, identify the closest approximate amount the first customer’s investment was worth after four years, and the difference in value of each customer’s investment after four years. Make two selections.
  • a)
    3
  • b)
    30
  • c)
    160
  • d)
    100
  • e)
    130
Correct answer is option 'A,C'. Can you explain this answer?
Most Upvoted Answer
Clearwater State Bank is offering an introductory 20% interest rate on...
The answer is 160 and 3. Customer 1 deposits $100 initially into the new account. If the amount P is invested at an annual interest rate of r percent, compounded n times per year, then the value V of the investment at the end of t years is given by the formula:

So after two years, the investment will be worth $146.41. That amount is then compounded annually for two more years at the adjusted rate of 5%. This formula becomes V = 146.41(1 + .05)2. This becomes V = 161.42. Customer 1’s investment is worth approximately $161 after four years, which is closest to 160 in the table.
Customer 2 had an equal amount after two years, so he/she would also have $146.41. Then the interest is compounded quarterly for the next two years at 6%. The formula for this would look like:

That is a difference of 164.93 – 161.42 = 3.51, which is closest to 3.
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Clearwater State Bank is offering an introductory 20% interest rate on...
Customer 1's Investment:
- The initial deposit is $100.
- The account compounds semi-annually at a rate of 20% for the first two years.
- After two years, the account compounds annually at a rate of 5%.

Calculating the Investment after Four Years:
- For the first two years: $100 * (1 + 0.20/2)^4 = $100 * (1.10)^4 ≈ $146.41
- For the next two years: $146.41 * (1 + 0.05) ^ 2 ≈ $160.16

Customer 2's Investment:
- The initial deposit is unknown.
- The account compounds quarterly at a rate of 15% for the first year.
- After the first year, the account compounds quarterly at a rate of 6%.

Calculating the Investment after Four Years:
- For the first year: Initial deposit * (1 + 0.15/4)^4 = Initial deposit * (1.0375)^4
- After the first year: (Initial deposit * (1.0375)^4) * (1 + 0.06/4)^12

Comparison:
- After four years, Customer 1's investment is approximately $160.16.
- The difference in value between the two customers' investments after four years is approximately $160.16 - Initial deposit for Customer 2.
Therefore, the closest approximate amount the first customer's investment was worth after four years is around $160, and the difference in value of each customer's investment after four years is approximately $160.
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Clearwater State Bank is offering an introductory 20% interest rate on a new account, which will compound semi-annually for the first two years, then compound 5% annually thereafter. Customer 1 deposits $100 in that account to start. To compete, Clearwater Credit Union is offering a similar offer. Their newest account offers an introductory rate of 15% compounded quarterly for the first year, and a rate of 6% compounded quarterly thereafter. Customer 2 deposits an unknown amount with Clearwater Credit Union. After two years, the customers had an equal amount saved.Q. From the choices below, identify the closest approximate amount the first customer’s investment was worth after four years, and the difference in value of each customer’s investment after four years. Make two selections.a)3b)30c)160d)100e)130Correct answer is option 'A,C'. Can you explain this answer?
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Clearwater State Bank is offering an introductory 20% interest rate on a new account, which will compound semi-annually for the first two years, then compound 5% annually thereafter. Customer 1 deposits $100 in that account to start. To compete, Clearwater Credit Union is offering a similar offer. Their newest account offers an introductory rate of 15% compounded quarterly for the first year, and a rate of 6% compounded quarterly thereafter. Customer 2 deposits an unknown amount with Clearwater Credit Union. After two years, the customers had an equal amount saved.Q. From the choices below, identify the closest approximate amount the first customer’s investment was worth after four years, and the difference in value of each customer’s investment after four years. Make two selections.a)3b)30c)160d)100e)130Correct answer is option 'A,C'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about Clearwater State Bank is offering an introductory 20% interest rate on a new account, which will compound semi-annually for the first two years, then compound 5% annually thereafter. Customer 1 deposits $100 in that account to start. To compete, Clearwater Credit Union is offering a similar offer. Their newest account offers an introductory rate of 15% compounded quarterly for the first year, and a rate of 6% compounded quarterly thereafter. Customer 2 deposits an unknown amount with Clearwater Credit Union. After two years, the customers had an equal amount saved.Q. From the choices below, identify the closest approximate amount the first customer’s investment was worth after four years, and the difference in value of each customer’s investment after four years. Make two selections.a)3b)30c)160d)100e)130Correct answer is option 'A,C'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Clearwater State Bank is offering an introductory 20% interest rate on a new account, which will compound semi-annually for the first two years, then compound 5% annually thereafter. Customer 1 deposits $100 in that account to start. To compete, Clearwater Credit Union is offering a similar offer. Their newest account offers an introductory rate of 15% compounded quarterly for the first year, and a rate of 6% compounded quarterly thereafter. Customer 2 deposits an unknown amount with Clearwater Credit Union. After two years, the customers had an equal amount saved.Q. From the choices below, identify the closest approximate amount the first customer’s investment was worth after four years, and the difference in value of each customer’s investment after four years. Make two selections.a)3b)30c)160d)100e)130Correct answer is option 'A,C'. Can you explain this answer?.
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