Final answer:
To find the final amount of a 5-year CD with $850 at 3.5% interest compounded annually, use the formula A = P(1 + r/n)^(nt). Calculate this with the values $850, 3.5% interest, compounded annually for 5 years to get the final amount at the CD's maturity.
Step-by-step explanation:
When you purchase a 5-year certificate of deposit (CD) with $850 that pays 3.5% interest compounded annually, the formula to calculate the final amount is: A = P(1 + r/n)nt. Here, A represents the amount of money accumulated after n years, including interest. P is the principal amount ($850), r is the annual interest rate (3.5% or 0.035), n is the number of times that interest is compounded per year (1, since it's compounded annually), and t is the time the money is invested for (5 years).
The calculation would be: A = $850(1 + 0.035/1)1*5 = $850(1 + 0.035)5 = $850(1.035)5. Now we just need to calculate (1.035)5 and multiply that by $850 to get the final amount.
If you compare the situation to a similar CD with $1,000 at 2% interest, compounded annually, the principle of calculating the final amount after five years is identical, but the numbers used in the formula are different: A = $1000(1 + 0.02)5. This illustrates how compound interest works for CDs and why they are considered a secure investment option, paying slightly higher interest rates than savings accounts as compensation for the lack of liquidity. When the CD matures after five years, you will receive your initial investment plus the interest that has accumulated over time.