4. Annie finds another bank, Star Bank, that offers a CD account with a 2% interest rate every month. Star Bank's interest is not compounded. The interest is based on the original amount of deposit. Remember that Annie has $500 to start the account. She will not withdraw or deposit more money in the account for 2 years.
(a) Fill in the table showing the amount of money in the Star Bank CD account over 4 months. 2 points
Months 0 1 2 3 4
Amount in CD account $500 $510 $520.2 $530.6 $541.22
(b) If Annie graphed the relation, what would the y-intercept be? Explain how you know this? 1 point
(c) Is the relation a function? Explain why or why not. 1 point
(d) Is the relation linear? Explain how you know this. If so, state the rate of change and write the equation of the relation, where x is the number of months and y is the amount in the account. If not, give a clear explanation as to why not. 2 points
(e) Annie plans to keep her CD account for 2 years. Which bank would you suggest Annie open her account with. Explain why you think that opening the account with that bank is the better deal.
To fill in the table for the amount of money in the Star Bank CD account over 4 months, we need to use the given interest rate of 2% per month. The interest is not compounded, so it is based on the original amount of deposit.
(a) Here is how to calculate the amount in the CD account for each month:
Month 0: Starting with $500.
Month 1: Add 2% of $500 to the original amount: $500 + (0.02 * $500) = $510.
Month 2: Add 2% of $500 to the original amount again: $500 + (0.02 * $500) = $510.
Month 3: Repeat the same calculation: $500 + (0.02 * $500) = $510.
Month 4: Once more, add 2% of $500 to the original amount: $500 + (0.02 * $500) = $510.
Therefore, the table for the amount of money in the Star Bank CD account over 4 months is as follows:
Months 0 1 2 3 4
Amount $500 $510 $520.2 $530.6 $541.22
(b) The y-intercept represents the value of the dependent variable (amount in the CD account) when the independent variable (months) is equal to zero. In this case, when the number of months is zero, the amount in the CD account is $500. Therefore, the y-intercept would be at point (0, $500).
(c) Yes, the relation is a function. A function is a relation in which each input (x-value) corresponds to exactly one output (y-value). In this case, for each month value (input), there is only one corresponding amount in the CD account (output).
(d) The relation is linear. A linear relation is a relation where the rate of change is constant. In this case, the amount in the CD account increases by a fixed amount of $10 per month. The rate of change is therefore constant at $10 per month.
The equation of the relation is y = mx + b, where m is the rate of change and b is the y-intercept. In this case, m (rate of change) is $10 per month, and b (y-intercept) is $500. Therefore, the equation of the relation is: y = 10x + 500.
(e) Considering the interest rates and the compounding frequency, it appears that Annie would be better off opening her account with Star Bank. Star Bank offers a 2% interest rate every month, while the other bank's interest rate is not given. Plus, Star Bank's interest is not compounded, meaning it is based on the original amount deposited, which will result in less accumulated interest over time compared to compounded interest. Therefore, Star Bank seems like the better deal for Annie's 2-year plan.