Suppose \( \$ 1,100 \) dollars is deposited into an account which has an annual percentage rate of \( 7.4 \% \) per year. Assume the interest is compounded annually. (a) Complete the boxes below to write a formula for the amount \( Q \) (in dollars) at year \( t \ ). Do not type any rounded values in these boxes. \( Q= \) Number

To calculate the amount \( Q \) in the account after \( t \) years with annual compounding interest, you can use the formula: \[ Q = P(1 + r)^t \] Where: - \( P \) is the principal amount (initial deposit), which is \( 1,100 \) dollars. - \( r \) is the annual interest rate in decimal form, so \( 7.4\% = 0.074 \). - \( t \) is the number of years the money is invested or borrowed. Plugging in the values, the formula becomes: \[ Q = 1100(1 + 0.074)^t \] Now, you can simplify it: \[ Q = 1100(1.074)^t \] This gives you the complete formula for the amount \( Q \) after \( t \) years. --- In the realm of finance, the magic of compound interest often leads to what is known as "the snowball effect." Picture this: just like rolling a small snowball down a snowy hill, as time goes on, that tiny investment can grow exponentially larger as interest is added not just to your initial deposit, but also to the interest that has already been accrued. With patience and time, your investment can surprise you! If you're ever in doubt about how long it might take for your investments to double, there's a fun rule called the Rule of 72. Simply divide 72 by your annual interest rate (in percentage), and you'll get an approximate number of years it will take for your investment to double. For a 7.4% interest rate, it would take about 9.7 years! Happy investing!