Leona is accepted to attend Monash University this year. She anticipates she will need $25,000 at the beginning of each of the four years at university to pay for university expenses.
a) Find the present value of Leonas university expenses assuming annual compounding and the interest rate remains at 8% p.a. during her university years. [3 marks]
b) 7 years ago, Leona had arranged with her Dad to do household chores if her Dad deposited $650 at the end of each month in a bank account paying 9% p.a. Assume the interests were calculated and paid monthly.
i) Find the amount available in the account today. Briefly explain whether this amount is enough for Leona to pay for her university expenses. [4 marks]
ii) If her Dad had deposited $650 at the beginning instead of the end of each month, without calculation, explain whether the amount today is larger or smaller than the answer in b)i) [3 marks]
iii) If her Dad had deposited $900 at the end of each month in the account, given your answer to part a), find the Annual Percentage Rate the account must earn so as to meet Leonas university expenses. [4 marks]
iv) Instead of making monthly deposits of $650 at the end of each month and earning 9% p.a, Leonas Dad would like to make the bank account deposits annually and interests are calculated and earned once a year.
- Find the effective annual rate that would make her Dad indifferent to these two ways of payment.
- Using the effective annual rate as above, find the annual deposit amount that would accumulate the same account balance as the answer in part b)i). [3+3=6 marks]
Please answer the following questions. Show all your workings when calculations are required and round off your FINAL result to TWO decimal places. Leona is accepted to attend Monash University this year. She anticipates she will need $25,000 at the beginning of each of the four years at university to pay for university expenses. a) Find the present value of Leona's university expenses assuming annual compounding and the interest rate remains at 8% p.a. during her university years. [3 marks] b) 7 years ago, Leona had arranged with her Dad to do household chores if her Dad deposited $650 at the end of each month in a bank account paying 9% p.a. Assume the interests were calculated and paid monthly i) Find the amount available in the account today. Briefly explain whether this amount is enough for Leona to pay for her university expenses. [4 marks] ii) If her Dad had deposited $650 at the beginning instead of the end of each month, without calculation, explain whether the amount today is larger or smaller than the answer in bi) [3 marks] iii) If her Dad had deposited $900 at the end of each month in the account, given your answer to part a), find the Annual Percentage Rate the account must earn so as to meet Leona's university expenses. (4 marks) iv) Instead of making monthly deposits of $650 at the end of each month and earning 9% p.a, Leona's Dad would like to make the bank account deposits annually and interests are calculated and earned once a year. Find the effective annual rate that would make her Dad indifferent to these two ways of payment. . Using the effective annual rate as above, find the annual deposit amount that would accumulate the same account balance as the answer in part b)i). (3+3=6 marks] Please answer the following questions. Show all your workings when calculations are required and round off your FINAL result to TWO decimal places. Leona is accepted to attend Monash University this year. She anticipates she will need $25,000 at the beginning of each of the four years at university to pay for university expenses. a) Find the present value of Leona's university expenses assuming annual compounding and the interest rate remains at 8% p.a. during her university years. [3 marks] b) 7 years ago, Leona had arranged with her Dad to do household chores if her Dad deposited $650 at the end of each month in a bank account paying 9% p.a. Assume the interests were calculated and paid monthly i) Find the amount available in the account today. Briefly explain whether this amount is enough for Leona to pay for her university expenses. [4 marks] ii) If her Dad had deposited $650 at the beginning instead of the end of each month, without calculation, explain whether the amount today is larger or smaller than the answer in bi) [3 marks] iii) If her Dad had deposited $900 at the end of each month in the account, given your answer to part a), find the Annual Percentage Rate the account must earn so as to meet Leona's university expenses. (4 marks) iv) Instead of making monthly deposits of $650 at the end of each month and earning 9% p.a, Leona's Dad would like to make the bank account deposits annually and interests are calculated and earned once a year. Find the effective annual rate that would make her Dad indifferent to these two ways of payment. . Using the effective annual rate as above, find the annual deposit amount that would accumulate the same account balance as the answer in part b)i). (3+3=6 marks]
