Tom invests $10,000 into two accounts, one paying 2% interest per year and the other paying 5% interest per year. He invested 3 times as much in the account paying 5% than in the account paying 2%. how much interest will he ear in one year?
if x at 2%, then the rest (10000-x) at 5%. So,
10000-x = 3x
so solve for x, and the interest earned is
.02x + .10(3x) = ?
To determine the interest Tom will earn in one year, we need to calculate the interest earned by each account and then sum them up.
Let's first find the amount invested in the account paying 2% interest. We know that Tom invested 3 times less in this account than in the 5% account. Let's assume he invested x dollars in the 2% account. Therefore, he invested 3x dollars in the 5% account.
The interest earned by the 2% account can be calculated by multiplying the principal (x) by the interest rate (2%) and converting it to a decimal: 0.02. So, the interest earned by the 2% account is 0.02x.
The interest earned by the 5% account can be calculated by multiplying the principal (3x) by the interest rate (5%) and converting it to a decimal: 0.05. So, the interest earned by the 5% account is 0.05 * 3x = 0.15x.
Now, let's sum up the interest earned by both accounts:
Interest = Interest from 2% account + Interest from 5% account
Interest = 0.02x + 0.15x
Now, we can substitute the value of x with the amount invested in the 2% account. Since Tom invested $10,000 in total, the amount invested in the 2% account is ($10,000 / (1 + 3)).
Therefore, the equation becomes:
Interest = 0.02 * ($10,000 / (1 + 3)) + 0.15 * ($10,000 / (1 + 3))
Now we can simplify and solve the equation to find the interest earned by Tom in one year.