Final answer:
The student's original emergency fund was $10,579.50 after saving for six months. After three years at a 4.5% APR, the balance before withdrawal is approximately $12,118.03. Following a withdrawal of $4,360, the balance would be around $7,758.03; however, the question's multiple-choice answers may contain errors as none match these calculations, so it is not possible to accurately provide the exact balance or lost interest without the correct options.
Step-by-step explanation:
The question involves calculating the remaining balance in a savings account earning annual compound interest after a withdrawal, and determining the lost interest due to that withdrawal. Given the fixed expenses of $1,763.25 a month, the student saved this amount for 6 months to create an emergency fund. This provides an initial deposit of $1,763.25 × 6 = $10,579.50. Given that the APR is 4.5%, compounded annually over 3 years, we need to apply the formula for compound interest to find the balance before the withdrawal:
A = P(1 + rac{r}{n})^{nt}
Where:
- A is the amount of money accumulated after n years, including interest.
- P is the principal amount (the initial amount of money).
- 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.
Using the formula, we find the balance before the withdrawal:
A = $10,579.50 (1 + rac{0.045}{1})^{1×3} = $10,579.50 (1 + 0.045)^{3} ≈ $12,118.03
After withdrawing $4,360.00 because of unemployment, the new balance is:
$12,118.03 - $4,360 = $7,758.03
To find how much interest was lost in one month due to the withdrawal, we would need to calculate the interest on the old balance (before withdrawal) for one month and subtract the interest on the new balance (after withdrawal) for one month. However, since we're given multiple-choice options and none of them could be reached with the calculated withdrawal, it appears there might be an error in the provided balances and interest rates or the question's options. Without the correct figures or more specific information, it's not possible to accurately determine the answers to the two parts of the question.