Finance - Series - Loan repayments TYS 1

Although the context here is on loans, some of these questions can focus on analogous situations where an investment fund has been established and regular payments are made from that fund. This would be the case with many superannuation accounts for example. Interest is paid on the balance in the fund but there is no further deposit of capital into the fund. Prize funds are similar.

The questions on this page focus on:

1. finding a repayment amount for a Loan.

2. finding the amount to be borrowed.

Finding a repayment amount.	1. Louise and Nigel are planning to buy a small house in the country. They will have to borrow $300,000 to buy it. They agree to repay the loan in equal monthly installments of $P over 20 years. Interest is charged at 6% p.a. (i) Show that the amount Louise and Nigel owe at the end of the 2^nd month can be expressed as A₂ = 300,000 × 1.005² - P(1 + 1.005) (ii) Hence calculate the value of the monthly installments $P. Answer.(ii) $2,149.29 monthly.
	2. David is saving to buy a new car. He is planning to spend $16,000 on the car. He already has $7,500 saved and he did consider putting an increasing amount of money aside from his wages on a monthly basis. This amount would be subject to a monthly interest rate of 0.5% p.m. As that proposition was not going to be satisfactory, he is now considering taking out a car loan. The bank suggested he retain $2,500 from his savings to cover other purchase expenses. They therefore offered a loan of $11,000 on a weekly repayment option for 4 years at 8% p.a. interest weekly reducible. (i) How much would the repayments cost David each week? (ii) Comment of that amount compared to his first plan of saving for his $16,000 car and then paying cash. Answer.(i) $61.84 weekly.
	3. A company owes $14 million dollars in tax payments to the Australian Tax Office. It agreed to repay that amount over two years in 24 equal installments. The legal shortfall interest rate of 4.54% p.a., as fixed by law, will be charged. What monthly repayments will be necessary to clear the debt in the required time? Answer.(i) $611,294.41 monthly.
	4. Megan borrows $10,000 and arranges to repay her loan in 20 equal instalments of $R every three months over 5 years. She is charged interest on the reducible loan at the rate of 8% p.a. (i) Show that, at the end of the second quarter, Megan still owes . (ii) How much will Megan have to repay each quarter? (iii) At the end of the loan, how much interest will Megan have paid? Answer.(ii) $611.57 quarterly. (iii) Interest = $2,231.40
	5. Charlotte has recently bought a number of items for her new home unit (now she has moved out of home :-). Unfortunately she has now reached her $2,000 limit on her credit card on which she has an interest rate of 12% p.a. charged on her balance at the end of each week (so 0.00231 p.w.). (i) What will Charlotte's weekly repayments be if she makes weekly deposits on her the credit card throughout the 52 weeks? (ii) How much interest will she have paid in the year? (iii) Show the balance of Charlotte's debt after 26 weeks is $1,030.04. (iv) After 6 months (26 weeks) of repayments, Charlotte decides to charge $50 per week to her card but increases her repayments to $50 per week on the assumption that her new strategy would simply balance her transactions and her credit card balance would still therefore be zero. Determine the balance outstanding on the credit card at the end of week 28 (two weeks after the new strategy starts). (v) Calculate the balance on the credit card at the end of week 48. Explain why Charlotte's strategy is not a good one. Answer.(i) $40.86 weekly. (ii) Interest is $124.72. (iii) At end of week 27, balance is $982.42. (iv) At end of week 48, balance is $9.14.
Finding the amount to be borrowed.	6. Sam wants to take out a 3 year loan to assist him to establish a small business. His Bank will allow him to take out a reducing balance loan at 4% p.a. interest and monthly reducible. Sam estimates he can afford to repay $3,500 from the takings of his business at the end of each month to cover the loan and interest. How much can Sam borrow? Answer.Borrow to $118,619.16.
	7. Sophie wants to borrow from her Building Society to buy a small car to drive to her new hospitality job and to TAFE to attend her apprenticeship as a Chef. She plans to keep the car for 4 years and so make monthly repayments of $200. The Building Society charges her 3% p.a. monthly reducible. How much can Sophie borrow to enable her to buy a car? Answer.She can borrow $9,035.74.