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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)
    100
  • d)
    130
  • e)
    160
Correct answer is option 'A,E'. Can you explain this answer?
Verified 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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Most Upvoted Answer
Clearwater State Bank is offering an introductory 20% interest rate on...
Has saved after two years.

a) $115
b) $120
c) $125
d) $130
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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)100d)130e)160Correct answer is option 'A,E'. Can you explain this answer?
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