questions is attached
QUESTION 1 Today, Malorie takes out a 30-year loan of $200,000, with a fixed interest rate of 4.7% per annum compounding monthly for the first 3 years. Afterwards, the loan will revert to the market interest rate. Malorie will make monthly repayments over the next 30 years, the first of which is exactly one month from today. The bank calculates her current monthly repayments assuming the fixed interest rate of 4.7% will stay the same over the coming 30 years.? (a) Calculate the size of the repayment that the bank requires Malorie to make at the end of the first month.? (1 mark) (b) Calculate the loan outstanding at the end of the fixed interest period (i.e. after 3 years).? (c) Calculate the total interest Malorie pays over this fixed interest period.? (d) After the fixed interest period, the market interest rate becomes 5.7% per annum effective. Assuming the interest rate stays at this new level for the remainder of the term of the loan, calculate the new monthly instalment.? Question 2 Burt deposits $10,000 into a bank account today. The account earns 4.5% per annum compounding daily for the first 4 years, then 4.5% per annum compounded quarterly thereafter. No further deposits or withdrawals will be made. For this question, assume all months are of equal length and ignore leap years. (a) Calculate the account balance six months from today? (1 mark) (b) Calculate the account balance 4 years from today ? (c) Calculate the account balance 4.5 years from today? (d) Calculate the account balance 10 years from today? Question 3 A loan of $100,000 is made today. The borrower will make equal repayments of $881 per month with the first payment being exactly one month from today. The interest being charged on this loan is constant (but unknown). For the following two scenarios, calculate the interest rate being charged on this loan, expressed as a nominal annual rate in percentage. Give your answer as a percentage to 2 decimal places. (a) The loan is fully repaid exactly after 180 monthly repayments, i.e., the loan outstanding immediately after 180 repayments is exactly 0. (b) The term of the loan is unknown but it is known that the loan outstanding 2 years later equals to $87534. (1.5 marks) QUESTION 1 Today, Malorie takes out a 30-year loan of $200,000, with a fixed interest rate of 4.7% per annum compounding monthly for the first 3 years. Afterwards, the loan will revert to the market interest rate. Malorie will make monthly repayments over the next 30 years, the first of which is exactly one month from today. The bank calculates her current monthly repayments assuming the fixed interest rate of 4.7% will stay the same over the coming 30 years.? (a) Calculate the size of the repayment that the bank requires Malorie to make at the end of the first month.? (1 mark) (b) Calculate the loan outstanding at the end of the fixed interest period (i.e. after 3 years).? (c) Calculate the total interest Malorie pays over this fixed interest period.? (d) After the fixed interest period, the market interest rate becomes 5.7% per annum effective. Assuming the interest rate stays at this new level for the remainder of the term of the loan, calculate the new monthly instalment.? Question 2 Burt deposits $10,000 into a bank account today. The account earns 4.5% per annum compounding daily for the first 4 years, then 4.5% per annum compounded quarterly thereafter. No further deposits or withdrawals will be made. For this question, assume all months are of equal length and ignore leap years. (a) Calculate the account balance six months from today? (1 mark) (b) Calculate the account balance 4 years from today ? (c) Calculate the account balance 4.5 years from today? (d) Calculate the account balance 10 years from today? Question 3 A loan of $100,000 is made today. The borrower will make equal repayments of $881 per month with the first payment being exactly one month from today. The interest being charged on this loan is constant (but unknown). For the following two scenarios, calculate the interest rate being charged on this loan, expressed as a nominal annual rate in percentage. Give your answer as a percentage to 2 decimal places. (a) The loan is fully repaid exactly after 180 monthly repayments, i.e., the loan outstanding immediately after 180 repayments is exactly 0. (b) The term of the loan is unknown but it is known that the loan outstanding 2 years later equals to $87534. (1.5 marks)