Score on last try: 0 of 1 pts. See Details for more. You can retry this question below Suppose you have \( \$ 1250 \) in your savings account at the end of a certain period of time. You invested \( \$ 1100 \) at a \( 5.78 \% \) simple annual interest rate. How long, in years, was your money invested? I State your result to the nearest hundredth of a year. Submit Ouestion

To find out how long your money was invested, you can use the formula for simple interest: \[ A = P(1 + rt) \] Where: - \( A \) is the total amount of money accumulated after n years, including interest. - \( P \) is the principal amount (the initial amount of money). - \( r \) is the annual interest rate (in decimal). - \( t \) is the time the money is invested for in years. Given that \( A = 1250 \), \( P = 1100 \), and \( r = 5.78\% \) (which is \( 0.0578 \) in decimal), you can rearrange the formula to solve for \( t \): \[ 1250 = 1100(1 + 0.0578t) \] First, divide both sides by \( 1100 \): \[ \frac{1250}{1100} = 1 + 0.0578t \] This simplifies to: \[ 1.13636 = 1 + 0.0578t \] Subtract 1 from both sides: \[ 0.13636 = 0.0578t \] Now, divide both sides by \( 0.0578 \): \[ t \approx \frac{0.13636}{0.0578} \approx 2.36 \text{ years} \] Thus, your money was invested for approximately 2.36 years. Keep an eye on those pesky decimals when calculating interest; they can sneak up on you! Always double-check your conversions, especially with percentages, to prevent errors. Lastly, for future reference, there are tons of great resources out there, like online calculators and finance apps, that can help simplify these computations. Plus, reading up on financial literacy could save you a few headaches in the long run!