Samantha finds a bank, Star Bank, which 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 Samantha has $500 to start the account. She will not withdraw or deposit more money in the account for 2 years.
5. Fill in the table showing the amount of money in the Star Bank CD account over 4 months.
Months 0 1 2 3 4
Amount in CD account $500.00
6. Is the relation a linear function? 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, explain why not.
since the interest is not compounded and only based on the original deposit, she receives monthly interest of:
$500 * 0.02 = $10
mo-0: $500
mo-1: $510
mo-2: $520
mo-3: $530
mo-4: $540
Yes - linear function, since the rate of change is constant.
To fill in the table, we need to calculate the amount in the CD account for each month.
Since the interest is not compounded and is based on the original amount of deposit, we can calculate the amount using the formula:
Amount in CD account = Original deposit + (Original deposit * Interest rate)
In this case, the original deposit is $500 and the interest rate is 2% per month.
Let's calculate the amount for each month:
Month 0: Amount = $500 + ($500 * 0.02) = $510.00
Month 1: Amount = $500 + ($500 * 0.02) = $510.00
Month 2: Amount = $500 + ($500 * 0.02) = $510.00
Month 3: Amount = $500 + ($500 * 0.02) = $510.00
Month 4: Amount = $500 + ($500 * 0.02) = $510.00
Now, let's fill in the table:
Months | 0 | 1 | 2 | 3 | 4
Amount |$510.00 |$510.00 |$510.00 |$510.00 |$510.00
Based on the table, we can see that the amount in the CD account remains constant at $510.00 for each month.
Since the amount is constant and does not change with the number of months, the relation is not a linear function. In a linear function, the amount would increase or decrease at a constant rate.
Therefore, the rate of change is 0 and the equation of the relation for this specific case would be:
y = $510.00