Please answer Question 3 using Rstudio.
How Much Is Your Discovery Worth? When looking at the car loans issued by your branch over the last five years (2016 - 2020) you notice that the fixed payments were calculated with the 5/1-year ARM rate (MORTGAGE5US) instead of the four-year-car-loan rate (TERMCBAUTO48NS). This is because your predecessor has made a coding mistake (an OU graduate). Demonstrate how much your discovery is worth to the company: 1. Aggregate the interest rates to yearly rates by taking the yearly average and plot the two interest rates on the same graph. Explain the differences. 2. Your branch issues a total of $2,500,000 four-year car loans every year. The branch receives 97% of the fixed payments and writes off the remaining 3% due to default. Calculate how much Lending Tree loses from 2017 to 2024 due to the mistake, assuming the branch would have issued the same amount of loans without the mistake. Use the yearly average of the two interest rates to calculate the fixed payments and their differences. 3. Calculate the present value of the mistake. Use the yearly means of the 1-Year Treasury Rate (GS1) from 2017 to 2020 to compound past losses and use the 1-Year Treasury Rate of July 2021 to discount future losses. 4. You convince your boss that without you, Lending Tree would keep issuing car loans at the 5/1-year ARM rate instead of the four-year-car-loan rate until the infinite future. Calculate the present value of discovering this mistake. To calculate the present value, assume that the yearly losses of all future years are equal to the loss of 2021 calculated in part 2. You can use the perpetuity formula to derive the present value. Then subtract the discounted losses between 2022 to 2024 that are caused by loans issued in the past. Instead of the 1-Year Treasury Rate, use the 30-Year Treasury Rate (GS30) of July 2021 to discount the future, which duration is closer to that of a perpetual bond. How Much Is Your Discovery Worth? When looking at the car loans issued by your branch over the last five years (2016 - 2020) you notice that the fixed payments were calculated with the 5/1-year ARM rate (MORTGAGE5US) instead of the four-year-car-loan rate (TERMCBAUTO48NS). This is because your predecessor has made a coding mistake (an OU graduate). Demonstrate how much your discovery is worth to the company: 1. Aggregate the interest rates to yearly rates by taking the yearly average and plot the two interest rates on the same graph. Explain the differences. 2. Your branch issues a total of $2,500,000 four-year car loans every year. The branch receives 97% of the fixed payments and writes off the remaining 3% due to default. Calculate how much Lending Tree loses from 2017 to 2024 due to the mistake, assuming the branch would have issued the same amount of loans without the mistake. Use the yearly average of the two interest rates to calculate the fixed payments and their differences. 3. Calculate the present value of the mistake. Use the yearly means of the 1-Year Treasury Rate (GS1) from 2017 to 2020 to compound past losses and use the 1-Year Treasury Rate of July 2021 to discount future losses. 4. You convince your boss that without you, Lending Tree would keep issuing car loans at the 5/1-year ARM rate instead of the four-year-car-loan rate until the infinite future. Calculate the present value of discovering this mistake. To calculate the present value, assume that the yearly losses of all future years are equal to the loss of 2021 calculated in part 2. You can use the perpetuity formula to derive the present value. Then subtract the discounted losses between 2022 to 2024 that are caused by loans issued in the past. Instead of the 1-Year Treasury Rate, use the 30-Year Treasury Rate (GS30) of July 2021 to discount the future, which duration is closer to that of a perpetual bond
