The graph and table below give the monthly principal and interest payments for a mortgage from 1999 to 2004. Use this information to predict the payment for2005.
year Payment
1999 $578
2000 613
2001 654
2002 675
2003 706
2004 730
2005
how do I fugure this out? I know I do something withall the differences but don't know what
It is unclear to me why a mortgage payment would be steadily rising from year to year. No wonder the economy is such a mess!
You are probably right in thinking they expect you to use first or second differences to "extrapolate"
Let's complete the table.
1999 $578
----------35 <- first differences
2000 613 ... 6 <--2nd differences
----------41
2001 654 ... -20
----------21
2002 675 ... 10
----------31
2003 706 ... -7
----------24
2004 730 ... -3
----------21
2005 751
It makes no sense to me why the payment increase would go up some years and down in others. There is no sort of discernible trend. I chose to average the second differnces to predict the first difference between 2004 and 2005
To predict the payment for 2005 based on the given information, you can use the concept of linear regression. This involves finding a line of best fit that represents the general trend of the data. Once you have the equation for this line, you can substitute 2005 into the equation to estimate the payment.
Let's start by calculating the differences between consecutive years. These differences will help us identify the pattern or trend in the data.
Year Payment Difference
1999 $578 -
2000 $613 $35
2001 $654 $41
2002 $675 $21
2003 $706 $31
2004 $730 $24
Now, we can find the average difference over the given time period.
Average Difference = (35 + 41 + 21 + 31 + 24) / 5 = 30.4
Next, we can use this average difference to find the predicted payment for 2005. Since the payments have been increasing over time, we can assume that the pattern will continue.
Payment for 2005 = Payment for 2004 + Average Difference = $730 + $30.4 = $760.4
Therefore, the predicted payment for 2005 is $760.4.
Note: Linear regression provides an estimate based on the linear trend in the data. It assumes that the relationship between the independent variable (year) and the dependent variable (payment) is linear.