Final answer:
The value of the account after 8 years, with a $7,200 initial deposit, 3.2% annual interest, and a $5,000 deposit after 3 years, is approximately $14,699.11. However, this calculation does not match any of the provided options, suggesting an error in the question or options given.
Step-by-step explanation:
The student is asking about the future value of a savings account with interest compounded annually. Initially, Sinorice deposited $7,200 in an account with a 3.2% annual interest rate. After 3 years, the initial deposit has grown with interest, and an additional $5,000 is added to the account total. To find the value of the account after 8 years, we need to calculate the compound interest for the initial deposit over the first 3 years, add the second deposit, and then calculate the compound interest for the next 5 years on the total amount in the account.
- Calculate the value of the initial $7,200 after 3 years using the compound interest formula A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest; P is the principal amount ($7,200); r is the annual interest rate (0.032); and t is the time the money is invested for (3 years).
A = $7,200(1 + 0.032/1)^(1*3) = $7,674.85 (approx). - Add the additional $5,000 deposit after 3 years to get a new principal.
New Principal = $7,674.85 + $5,000 = $12,674.85. - Calculate the compound interest for the new principal over the next 5 years.
A = $12,674.85(1 + 0.032/1)^(1*5) = $14,699.11 (approx).
Thus, the value of the account after 8 years is approximately $14,699.11. However, none of the provided options match this value, which suggests there may be a typo or mistake in the options or in the calculation performed. Review the interest rates, the deposits, and the calculations to ensure accuracy.