He will deposit 1,500 into Account II, which earns 2% interest compounded annually. The teacher will not make any additional deposits or withdrawals . Which amount is closest to the total balance of these two accounts at the end of 4 years? 3,850.00 3,831.28 3,823.65 3,863.35

To find the total balance of the two accounts at the end of 4 years, we need to calculate the future value of the deposit in Account II using the compound interest formula.<br /><br />The compound interest formula is given by:<br /><br />\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \]<br /><br />where:<br />- \( A \) is the future value of the investment/loan, including interest<br />- \( P \) is the principal investment amount (the initial deposit or loan amount)<br />- \( r \) is the annual interest rate (decimal)<br />- \( n \) is the number of times that interest is compounded per year<br />- \( t \) is the time the money is invested or borrowed for, in years<br /><br />Given:<br />- \( P = \$1,500 \)<br />- \( r = 2\% = 0.02 \)<br />- \( n = 1 \) (since the interest is compounded annually)<br />- \( t = 4 \) years<br /><br />Plugging these values into the formula:<br /><br />\[ A = 1500 \left(1 + \frac{0.02}{1}\right)^{1 \cdot 4} \]<br />\[ A = 1500 \left(1 + 0.02\right)^4 \]<br />\[ A = 1500 \left(1.02\right)^4 \]<br /><br />Now, calculate \( (1.02)^4 \):<br /><br />\[ (1.02)^4 \approx 1.08243216 \]<br /><br />Then multiply by the principal amount:<br /><br />\[ A = 1500 \times 1.08243216 \]<br />\[ A \approx 1623.64824 \]<br /><br />So, the balance in Account II after 4 years will be approximately \$1,623.65.<br /><br />Since the teacher will not make any additional deposits or withdrawals, the total balance in Account II remains \$1,623.65.<br /><br />Therefore, the closest amount to the total balance of these two accounts at the end of 4 years is:<br /><br />\[ \boxed{3823.65} \]