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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 approximately how much extra Customer 1 would earn by keeping his money in Clearwater State Bank for four years versus two years, and also identify the difference in the final balances if he moved his investment to Clearwater Credit Union halfway through the four years. Make two selections.
  • a)
    15
  • b)
    `19
  • c)
    111
  • d)
    224
  • e)
    233
Correct answer is option 'A,B'. Can you explain this answer?
Most Upvoted Answer
Clearwater State Bank is offering an introductory 20% interest rate on...
The correct answers are 15 and 19. After two years, Customer 1’s $100 will have compounded at 10% four times: $110 after six months, $121 after one year, and $146.41 after two years.
The rate then changes to 5% annually, so after the third year that would be $146.41 * 1.05 = $153.73. And after the fourth year, Customer 1 would have $153.73 * 1.05 = $161.42.
“How much extra” Customer 1 earns is $161.42 − $146.41 = $15
If he moved to the Credit Union after two years, then that would be $146.41 compounded at 15% / 4 = 3.75% four times in the third year, and 6% /4 = 1.5% four times in the fourth year. You could use the formula for compounding interest as follows:

This second option would result in a final amount of $180.05, a difference of $18.63 (approximately $19) when compared with the earlier balance of $161.42.
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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 approximately how much extra Customer 1 would earn by keeping his money in Clearwater State Bank for four years versus two years, and also identify the difference in the final balances if he moved his investment to Clearwater Credit Union halfway through the four years. Make two selections.a)15b)`19c)111d)224e)233Correct answer is option 'A,B'. Can you explain this answer?
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