Jacob has not paid his $320 credit card bill and it was sent to collections. His
ID: 3029338 • Letter: J
Question
Jacob has not paid his $320 credit card bill and it was sent to collections. His interest rate is 43%, compounded daily.
1. Wrte an exponential function that models this situation where y is the balance of Jacob's account and x is time in years.
2. Use your equation from problem 24 to complete the chart to right; round to the nearest cent.
3. Use your data from problem 25 to graph your equation from problem 24. ( Use an x- scale of .5 years and a y- scale of $100.)
4. If Jacob left his account unpaid in 2009, calculate the expected balance in 2014 if he has not paid. Show your calulations and consider the trend of your graph above. (Recall that 2012 is a leap year.)
Explanation / Answer
1. If the daily interest is 43 %, then the balance due after 1 day is $ 320*(1+0.43)= 320*(1.43) so that the balance due after an year is 320*(1.43)365 and the balance after x years is 320*(1.43)365x.
There, however, appears to be some mistake here. Possibly the daily rate of interest is 0.43 % and not 43 %, for otherwise, the number of digits would be too large to compute even the interest for an year. If so, the interest for1day is $320*(1+0.0043) = 320*(1.0043) and the interest for x years is 320*(1.0043)365x.
2. The problem 24 is not described here. Therefore, we do not know the chart and cannot complete it.
3. The problem 25 is not described here. Therefore, we cannot prepare the graph.
4. If Jacob left his account unpaid in 2009, his expected balance in 2014 would be (if the daily interest rate of 0.43 %), the interest for 5 years i.e. for 365*5 = 1825 days. However, since 2012 is a leap year, making corresponding adjustment, the number of days becomes 1825 +1 =1826. Then the balance in 2014 would be 320*(1.0043)1826 = 320*2.527451768 =$ 808.78 ( on rounding off to the nearest cent). However, if the daily rate of interest is 43 %, then the balance after 1826 days would be $ 320*(1.43)1826 . The trend in the graph cannot be described for the above reasons.
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