Final answer:
To find out how much to initially deposit in a bank account to achieve $10,000 after 10 years at 10% compound interest, you rearrange the future value formula to solve for the principal. The correct initial deposit is calculated using the formula Principal = Future Value / (1 + interest rate)^time. In this case, you would calculate Principal = $10,000 / (1 + 0.10)^10.
Step-by-step explanation:
To calculate the future value of an annuity, we use the formula Future Value = Principal × (1 + interest rate)^time. In this case, the student is expected to find the future value of an annuity where $4,000 is deposited at the end of each quarter for 10 years with an interest rate of 6%, compounded quarterly. The future value can be obtained by using the Future Value of Ordinary Annuity table provided or by applying the formula for the future value of an annuity if the table is not available.
However, if the student wishes to find out how much money should be initially deposited in a bank account to have $10,000 after 10 years at an interest rate of 10% compounded annually, the formula Future Value = Principal × (1 + interest rate)^time can be rearranged to solve for the principal, which represents the initial deposit needed. The adjusted formula is Principal = Future Value / (1 + interest rate)^time. By applying this formula, the student will arrive at the amount to be initially deposited.
The calculation would look similar to this: Principal = $10,000 / (1 + 0.10)^10 which after calculation gives the present value needed to achieve the future value of $10,000 in ten years at a 10% annual compound interest rate.