Question

Suppose $5,000 is divided into two bank accounts. One account pays 5% simple interest per year and the other pays 7% per year. If after one year there is a total of $310 in interest between the two accounts, $3,000 was invested at 5%

Answer 1

The interest earned by the additional amount invested in the 5% is $290

Step-by-step explanation:

To solve this problem, we can set up an equation based on the information given.

Let x represent the amount of money invested at 7%. Since $3,000 was invested at 5%, we can conclude that $2,000 was invested at 7%.

The interest earned from the $5,000 is the sum of the interest earned from the two accounts. From the information given, we know that the total interest earned is $310.

We can use the formula for simple interest: I = P * r * t, where I is the interest, P is the principal amount, r is the interest rate, and t is the time in years.

For the account with 5% interest, we have I5% = (3,000)(0.05)(1) = $150.

For the account with 7% interest, we have I7% = (2,000)(0.07)(1) = $140.

Therefore, the total interest earned is $150 + $140 = $290.

Since there is a difference of $310 - $290 = $20, we can conclude that this $20 difference must have come from the interest earned by the additional $2,000 invested in the account with 5% interest.

So, to summarize, $3,000 was invested at 5%, and $2,000 was invested at 7%.

The total interest earned is $290.