Quations You invested \( \$ 21,000 \) in two accounts paying \( 2 \% \) and \( 5 \% \) annual interest, respectively. If the total interest earned for the year \( 60 \%, 9 \) of 15 points was \( \$ 810 \), how much was invested at each rate? The amount invested at \( 2 \% \) is \( \$ \square \).

To solve this problem, we first need to define variables for the amounts invested in each account. Let \( x \) be the amount invested at \( 2\% \) and \( 21000 - x \) be the amount invested at \( 5\% \). According to the problem, the total interest earned from both accounts is \( 810 \). We can set up the equation for the total interest: \[ 0.02x + 0.05(21000 - x) = 810 \] Now let's simplify and solve for \( x \): \[ 0.02x + 1050 - 0.05x = 810 \] Combining like terms gives: \[ -0.03x + 1050 = 810 \] Subtract \( 1050 \) from both sides: \[ -0.03x = -240 \] Now divide by \( -0.03 \): \[ x = 8000 \] Thus, the amount invested at \( 2\% \) is \( \$ 8,000 \). To find the amount invested at \( 5\% \), subtract \( 8,000 \) from \( 21,000 \): \[ 21000 - 8000 = 13000 \] Therefore, \( 13000 \) was invested at \( 5\% \). In conclusion, the amount invested at \( 2\% \) is \( \$ 8,000 \) and the amount invested at \( 5\% \) is \( \$ 13,000 \). For some added fun in finance: Did you know that the concept of interest dates back to ancient Mesopotamia? Sumerians began recording transactions that involved loans and interest rates as early as 3000 BC! They used a form of barley as currency! And if you're interested in how interest affects your savings, you might want to check out the "Rule of 72." This nifty math trick can help you estimate how long it will take for your investment to double at a specific interest rate. Just divide 72 by your annual interest rate, and voilà!