A bank offers a CD that pays a simple interest rate of $3.5 \%$. How much must you put in this $C D$ now in order to have $\$ 2000$ for a graduation trip in 4 years?
Answer
Final Answer: The amount that must be deposited now in order to have $2000 for a graduation trip in 4 years is approximately \$1754.39. Therefore, the final answer is \(\boxed{1754.39}\).
Step 1 ：The problem is asking for the initial amount to be deposited in a bank that offers a simple interest rate of 3.5% per annum in order to have $2000 in 4 years.
Step 2 ：The formula for simple interest is: \[ A = P(1 + rt) \] 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 (in decimal form), and t is the time the money is invested for, in years.
Step 3 ：We can rearrange the formula to solve for P: \[ P = \frac{A}{1 + rt} \]
Step 4 ：We know that A = $2000, r = 3.5% = 0.035 (in decimal form), and t = 4 years. We can substitute these values into the formula to find P.
Step 5 ：After executing the calculation, we get P = 1754.3859649122805
Step 6 ：The result from the calculation is approximately 1754.39. This means that in order to have $2000 in 4 years with an annual interest rate of 3.5%, we need to deposit approximately $1754.39 now. This result makes sense in the context of the problem.
Step 7 ：Final Answer: The amount that must be deposited now in order to have $2000 for a graduation trip in 4 years is approximately \$1754.39. Therefore, the final answer is \(\boxed{1754.39}\).
