Word Problem - Investments

Question

A total of $5000 was invested in two accounts. One pays 5% annual interest, and the second pays 7% annual interest. If the first-year interest is $325, how much was invested in each account?

Answer 1

Hi.

To solve this problem, we have to keep in mind that the interest earned in that first year - $325 - is the amount of interest earned by both accounts together.

Now we write an equation to reflect that understanding. Let's call the first account A and the second account B. We know that the annual interest rate on A is 5 percent and the annual interest rate on B is 7 percent. So:

0.05A + 0.07B = $325

We also know that the principal in both accounts together is $5,000.

So:

A + B = $5,000

So A = 5,000 - B

Now let's substitute that into the equation we wrote:

.05(5,000 - B) + .07B = 325

250 - .05B + .07B = 325

.02B = 75

B = $3,750

If B = $3,750, then A = $5,000 - $3,750 = $1,250

Now we can figure out the interest on each account:

.05A + .07B = $325

.05 ($1,250) + .07 ($3,750) = $325

A = $62.50

B = $262.50

Account A earned $62.50 in interest during the year, while account B earned $262.50 in interest during the year.