Question

3.4.13
E Question Help
Scott invested a total of $5900 at two separate banks. One bank pays simple interest of 12% per year while the other pays simple interest at a rate of 6% per year. If
Scott earned $540.00 in interest during a single year, how much did he have on deposit in each bank?
Scott had $ 2,800 on deposit at the bank that payed 12% interest.

Answer 1

Answer:

• $3100 at 12%
• $2800 at 6%

Step-by-step explanation:

Let x represent the amount on deposit at 12%. Then 5900-x is the amount deposited at 6%, and the total interest earned is ...

  12%·x +6%·(5900 -x) = 540

  0.06x + 354 = 540 . . . . . . . . eliminate parentheses

  0.06x = 186 . . . . . . . . . . . . . . subtract 354

  x = 3100 . . . . . . . . . . . . . . . . . divide by 0.06

Scott invested $3100 at 12% and $2800 at 6%.

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Quick sanity check

The average interest earned is $540/$5900 ≈ 0.0915 ≈ 9.15%. This is more than the average of 12% and 6%, which is (12+6)/2 = 9 percent. Hence more than half of the money must be deposited at 12%.