lheiannie07 wrote: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 compound interest. If both accounts have the same balance after two years, what is the value of r?
A. 11
B. 14.25
C. 18.5
D. 20
E. Cannot be determined
Let the savings in each account = 100.
In the account with simple annual interest of 22%:
Total after the first year = 100 + (22% of 100) = 100+22 = 122.
Total after the second year = 122 + (22% of 100) = 122+122 = 144.
For the account with r% COMPOUNDED annual interest, we can PLUG IN THE ANSWERS, which represent the value of r.
After two years, the account with compounded annual interest must hold $144 -- the same amount yielded by the account with simple annual interest.
D: 20%
Total after the first year = 100 + (20% of 100) = 100+20 = 120.
Total after the second year = 120 + (20% of 120) = 120+24 = 144.
Success!
The correct answer is
D.
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