Alan has split his savings equally into two accounts. The first one is a simple interest savings account with 22% annual interest, and the other is a savings account with $$r\%$$ annual interest compounded annually. If both accounts have the same balance after two years, what is the value of $$r$$?

Incorrect.
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Incorrect.
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Incorrect.
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Incorrect.
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Correct.
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First, find the balance in the simple interest account after 2 years at 22% simple interest. If $100 is deposited in each account, then the balance will be
>$$ $100 + $22$$ (first year) $$+ $22$$ (2nd year) $$= $144$$.
Now assume that $$r$$, the interest in the compound interest account, is 20% (answer choice D). Calculate the balance in the second account in each year:
- After the first year, the balance is $$\$100 + 20\% \text{ of } \$100 = \$120$$.
- After the second year, the balance is $$\$120 + 20\% \text{ of } \$120 = \$144$$.
Based on this, the balances in both accounts after two years are equal. Hence, this is the correct answer.

11

14.25

18.5

20

30