Hello, Baxter,
We need to decide how the $7000 is split between the two accounts. We have no idea, yet, so let's get around this obstacle by stating one account is worth X. That means the second account must be (7000-X). Whatever goes in the first must come from the second. That doesn't seem like much progress, but we now have accurate definitions for both accounts, so let's see what we can do with the fact that Salvador earned $370 in interest from the accounts.
I'll assume this is simple interest and was paid one, at the end of the year, when this questions was posed. We know that the two interest rates are 2% (0.02) and 12% (0.12). Let's say the 2% rate was for the account with X dollars and the 12% rate is the account with (7000-X) dollars. That means we can calculate the interest on the two accounts and then their interest sum is equal to $370:
Amount x Rate = Interest
X * 0.02 = 0.02X
(7000-X) * 0.12 = (0.12*(7000)-0.12X) or (840-0.12X)
When we add the two amounts, we will equal the $370 total interest that was reported.
0.02X + (840-0.12X) = 370
Combine terms
-0.10X = 370-840
-0.10X = - 470
X = 4700
(7000-X) = 2300
X was defined as the account earning 2% interest, so we have the following:
Account Value Interest Rate 1 Yr Interest
$4700 2% $94
$2300 12% $276
Total $370
So this works. What's surprising is that we could just as easily said the first account was the one earning 12%. We still get the same result: two accounts with the same amounts as above, only we arrived at the same conclusion going in reverse. As long as we're consistent in our definitions, we'll get the same answer.
Bob
