Final answer:
The ending balance after one year of $800 at an interest rate of 3.87% compounded quarterly is approximately $830.56. The closest answer choice provided is B. $830.00, taking into consideration rounding differences in the options or potential typos.
Step-by-step explanation:
To calculate the ending balance of $800 with an interest rate of 3.87% compounded quarterly after one year, we use the formula for compound interest:
A = P(1 + \frac{r}{n})^{nt}
Where:
- A is the amount of money accumulated after n years, including interest.
- P is the principal amount ($800).
- r is the annual interest rate (decimal).
- n is the number of times that interest is compounded per year.
- t is the time the money is invested for in years.
First, convert the interest rate from a percentage to a decimal:
3.87% = 0.0387
Next, plug the values into the formula:
A = $800(1 + \frac{0.0387}{4})^{4\times1} = $800(1 + 0.009675)^4
Calculating this gives:
A = $800(1.009675)^4 = $800 \times 1.0392 ≈ $830.56
This means the ending balance after one year is approximately $830.56, which was not one of the options provided. However, if we consider potential rounding differences in the options given or possible typo errors, the closest correct answer from the options would be B. $830.00.