An actor invests some money at 6​%, and ​$36,000 more than three times the amount at 7 %. The total annual interest earned from the investment is ​$23,460. How much did he invest at each​ amount?

Answer 1

The above is an excellent solution to the problem. However, I would have liked to have seen the answer verified.

$77,555.56 × 6% = $4,653.33

($36,000 + 3×$77,555.56) × 7% = $18,806.67

The sum of these two values is $23,460, which is exactly what the problem specified.

Checking your answer, in my opinion, should always be the last step in your solution process. As teachers we sometimes forget to emphasize this often enough.

Answer 2

the amount of simple interest earned in a year is calculated by applying the annual interest rate times the amount of the investment.

First Investment: Let P be the amount, @ 6% (0.06)

Second Investment: $36,000 more than three times the first investment is: 3P + 36,000, @ 7% (0.07)

First Investment interest + second investment interest = Total interest

0.06 x P + 0.07 x (3P + 36,000) = 23,460

0.06P + 0.21P + 2,520 = 23,460

0.27P = 20,940

P = 77,555.56 (first investment @ 6%)

3P = 232,666.67

3P + 36,000 = 268,666.67 (second investment total @7%)

Investment @ 6% = $77,555.56

Investment @ 7% = $268,666.67