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# Interest: Compound Interest

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. [[Snippet]]
Incorrect. [[Snippet]]
Incorrect. [[Snippet]]
Incorrect. [[Snippet]]
Correct. [[Snippet]] 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.
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14.25
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30