Elizabeth wants to have $\$ 20,500.00$ in 6 years so she can buy a new car. She found a credit union offering her a savings account with $3 \frac{1}{2} \%$ interest compounded weekly.
What does she need to deposit today in order to get her new car? Round your answer up to the nearest penny. Assume the interest rate remains constant while the accoun is open.
Answer
\(\boxed{\$16,618.16}\) is the final answer.
Step 1 ：Translate the given problem into the formula for the present value of an investment: PV = FV / (1 + r/n)^(nt).
Step 2 ：Identify the given values: Future Value (FV) is \$20,500, the annual interest rate (r) is 3.5% or 0.035 in decimal form, the number of times interest is compounded per year (n) is 52 (since it's compounded weekly), and the time the money is invested for (t) is 6 years.
Step 3 ：Substitute the given values into the formula: PV = 20500 / (1 + 0.035/52)^(52*6).
Step 4 ：Solve the equation to find the present value (PV).
Step 5 ：Round the answer to the nearest penny to find that Elizabeth needs to deposit \$16,618.16 today in order to have \$20,500 in 6 years.
Step 6 ：\(\boxed{\$16,618.16}\) is the final answer.
