1 Caysie deposits 1,500 into each of two savings accounts. Account I earns 5% annual simple interest. Account II earns 5% interest compounded annually. Caysie does not make any additional deposits or withdrawals. What in Account I and Account II at the end of 3 years?

To solve this problem, we need to calculate the amount of money in Account I and Account II at the end of 3 years.<br /><br />Given information:<br />- Caysie deposits $1,500 into each of two savings accounts.<br />- Account I earns 5% annual simple interest.<br />- Account II earns 5% interest compounded annually.<br />- Caysie does not make any additional deposits or withdrawals.<br /><br />Step 1: Calculate the amount in Account I at the end of 3 years.<br />The formula for simple interest is:<br />\[ A = P(1 + rt) \]<br />Where:<br />- \( A \) is the final amount<br />- \( P \) is the principal amount (initial deposit)<br />- \( r \) is the annual interest rate (in decimal form)<br />- \( t \) is the time in years<br /><br />For Account I:<br />\[ P = \$1,500 \]<br />\[ r = 0.05 \]<br />\[ t = 3 \]<br /><br />\[ A = 1500(1 + 0.05 \times 3) \]<br />\[ A = 1500(1 + 0.15) \]<br />\[ A = 1500 \times 1.15 \]<br />\[ A = \$1,725 \]<br /><br />Step 2: Calculate the amount in Account II at the end of 3 years.<br />The formula for compound interest is:<br />\[ A = P(1 + \frac{r}{n})^{nt} \]<br />Where:<br />- \( A \) is the final amount<br />- \( P \) is the principal amount (initial deposit)<br />- \( r \) is the annual interest rate (in decimal form)<br />- \( n \) is the number of times interest is compounded per year<br />- \( t \) is the time in years<br /><br />For Account II:<br />\[ P = \$1,500 \]<br />\[ r = 0.05 \]<br />\[ n = 1 \] (compounded annually)<br />\[ t = 3 \]<br /><br />\[ A = 1500(1 + \frac{0.05}{1})^{1 \times 3} \]<br />\[ A = 1500(1 + 0.05)^{3} \]<br />\[ A = 1500(1.05)^{3} \]<br />\[ A = 1500 \times 1.157625 \]<br />\[ A = \$1,728.94 \]<br /><br />Therefore, at the end of 3 years:<br />- The amount in Account I is $1,725.<br />- The amount in Account II is $1,728.94.