Final answer:
The future account balance of a $5000 principal amount after 4 years at a 3.75% interest rate compounded yearly is approximately $5,793.2. We use the compound interest formula, Principal (1 + interest rate)^time, to find the value, resulting in answer D.
Step-by-step explanation:
To calculate the future account balance with compound interest, the formula to use is: Principal (1 + interest rate)^time. In this case, we are given a principal amount of $5000, an interest rate of 3.75%, and a compounding period of 4 years. Since the interest is compounded yearly, we only compound once per year.
The interest rate in decimal form is 3.75% / 100 = 0.0375. Using the formula, the calculation for the future account balance is:
Future Account Balance = $5000 (1 + 0.0375)^4
Let's calculate it step by step:
- Calculate the growth factor: 1 + 0.0375 = 1.0375
- Raise the growth factor to the power of 4 (the number of years): (1.0375)^4
- Multiply the principal by the result from step 2 to find the future balance: $5000 * (1.0375)^4
After performing the calculations, the future account balance is approximately $5,793.2. Therefore, the correct answer from the provided options is D.