On 1 January 2022, a student plans to take out a 10-year bank loan for $15,000....

 

Transcribed Image Text:

On 1 January 2022, a student plans to take out a 10-year bank loan for $15,000. Under the repayment schedule, instalments will be paid monthly in arrears until the end of the term. The first instalment, at the end of January 2022, will be X, and the second instalment, at the end of February 2022, will be 2.X, and so on, until the instalment at the end of December 2026, which will be 60X. The remaining instalments from the end of January 2027 will also be 60X. The bank charges a rate of interest of 12% p.a. effective. (i) Write down an equation of value to calculate X. (ii) Calculate the value of X using the equation of value in part (i). (ii) Write down an equation to calculate the loan outstanding, after the instalment paid at the end of December 2026, using the retrospective method. (iv) Calculate the loan outstanding after the instalment at the end of December 2026 has been paid, using the equation in part (iii). (v) Comment on your answer to part (iv). (vi) Write down an equation to calculate the total interest paid during 2027. (vii) Calculate the total interest paid during 2027 using the equation in part (vi). [2 The bank also offers the 10-year loan with the same interest rate but where the monthly instalments remain level throughout the term. (viii) Comment on whether the total interest paid by the student under this revised offer would be greater or less than that paid under the original repayment [2 [Total 18 schedule. You should not perform any further calculations. On 1 January 2022, a student plans to take out a 10-year bank loan for $15,000. Under the repayment schedule, instalments will be paid monthly in arrears until the end of the term. The first instalment, at the end of January 2022, will be X, and the second instalment, at the end of February 2022, will be 2.X, and so on, until the instalment at the end of December 2026, which will be 60X. The remaining instalments from the end of January 2027 will also be 60X. The bank charges a rate of interest of 12% p.a. effective. (i) Write down an equation of value to calculate X. (ii) Calculate the value of X using the equation of value in part (i). (ii) Write down an equation to calculate the loan outstanding, after the instalment paid at the end of December 2026, using the retrospective method. (iv) Calculate the loan outstanding after the instalment at the end of December 2026 has been paid, using the equation in part (iii). (v) Comment on your answer to part (iv). (vi) Write down an equation to calculate the total interest paid during 2027. (vii) Calculate the total interest paid during 2027 using the equation in part (vi). [2 The bank also offers the 10-year loan with the same interest rate but where the monthly instalments remain level throughout the term. (viii) Comment on whether the total interest paid by the student under this revised offer would be greater or less than that paid under the original repayment [2 [Total 18 schedule. You should not perform any further calculations.

Answer rating: 100% (QA)

i The annual effective interest rate is 12 Monthly rate r 1 annual effective rate 112 1 112 112 1 09... View the full answer