Fred needs to buy the equipment shown in the table for his work as a tiler, but doesn’t have the necessary funds:
If Fred was able to pay by cash, what would the total cost be?
Fred uses a hire purchase at a simple interest rate of 7\% p.a. to pay for the equipment. If he pays 9 equal monthly instalments, how much more does he pay than if he had paid cash?
| Drill | \$250 |
|---|---|
| Tile cutter | \$300 |
| Polisher | \$500 |
| Circular saw | \$600 |
A store offers a 8\% discount to customers paying by cash.
If the retail price of a particular plasma TV is \$700 , what is the cash price?
A store offers a 9\% discount to customers paying by cash. If Luke purchases goods to the value of \$129 with cash, calculate:
The discount he receives.
The amount he has to pay.
Han purchases a drill selling for \$400 at a hardware store.
Calculate the amount he has to pay if he receives a trade discount of 7\%.
Calculate the amount he has to pay if he pays with cash and receives a further discount of 10\%.
The marked price of a particular grinder sold in a store is \$350.
If the store offered a store-wide discount of 12\% and a further discount of 7\% is applied to the discount price, to customers who paid by cash, how much was the cash price?
The following people purchased different items on lay-by. Find how much more they still need to pay for the item:
Maria's item was valued at \$165. She paid a deposit of \$16.00.
Dave's item was valued at \$418. He paid a deposit of 8\%.
James's item was valued at \$110. The deposit required was 5\% and the lay-by fee was \$17.
Han's item was valued at \$340. If he paid a deposit of \$5 and paid the balance off with weekly payments of \$30, after how many whole weeks will he receives ownership of the item?
Maria's item was valued at \$180. If she paid a deposit of 19\% and paid the balance off with fortnightly payments of \$26, how many fortnights are there until she receives ownership of the item?
Amelia's item was valued at \$110. If she paid a deposit of 22\% and paid the balance off with monthly payments of \$38, after how many full months will she receive ownership of the item?
The following people purchased different items on lay-by. Find the size of their regular payments:
Valentina's item was valued at \$200. She paid a deposit of 15\% and paid the balance off with regular weekly payments over 14 weeks.
Dave's item was valued at \$160. He paid a deposit of \$30 and paid the balance off with regular monthly payments over 3 months.
Valentina takes out a personal loan to purchase a motorbike valued at \$5000. The loan has an interest rate of 22.8\% p.a., compounded monthly.
How much will she owe after the first month?
If Valentina pays \$3829 between the first and second month. How much will she owe after the second month?
If she pays off the remaining amount after the third month, how much has she paid altogether?
How much more has she paid taking out a personal loan instead of using a debit card to pay for the car up front?
The sale price of a bike is \$800. Vincent chooses to purchase the item on credit card, with 16 days interest free. His card has an interest rate of 14\% per annum, compounded daily.
Vincent pays \$483 on his payment due date. How much does he still owe?
Vincent pays the remaining balance 22 days later. How much does he pay overall for the item?
How much more does Vincent pay by using his credit card instead of cash?
Skye purchases the following items online with 9 days of her interest free period left:
Skye uses her credit card to purchase the items and immediately pays off \$26. How much does she still owe?
| Journal | \$10 |
|---|---|
| Pencil case | \$10 |
| Stationery | \$5 |
| Mug | \$15 |
If her payment cycles are every 30 days and her card has an interest rate of 12\% p.a., how much will she owe at the end of the next payment cycle, assuming the cycle started at the end of the interest free period.
If she pays her outstanding balance at the end of that payment cycle, how much more does she pay compared to using her debit card to pay upfront?
For a particular credit card, the interest-free period for a payment occurs between the date of transaction and the payment due date following a new statement period.
Oprah purchases a computer game, and a controller and the timeline of events is shown below:
| Date | Action |
|---|---|
| 7 \text{ August} | \text{Start of statement period } 1 |
| 19 \text{ August} | \text{Bought computer game for } \$89 |
| 7 \text{ September} | \text{Start of statement period } 2 |
| 15 \text{ September} | \text{Bought controller for } \$91 |
| 22 \text{ September} | \text{Payment due date for statement period } 1 |
Oprah pays off \$30 on the day of purchase. How much is still owing 13 days after the payment due date (for statement period 1), if the interest rate is 15.35\% p.a., compounding daily?
If Oprah pays off the balance owing on her card 13 days after the payment due date, how much more has she paid as opposed to using cash to pay upfront for both items?
Alexia is interested in buying a new computer valued at \$1818.09. She doesn’t have the money to pay up front, but the store has an option to pay by hire purchase, with 12 equal monthly payments.
Alexia wants to avoid paying more than \$192 per month. What is the largest simple interest rate, R\% p.a., that Alexia would to agree to? Round your answer correct to two decimal places.
How much more does she pay using the hire purchase with this simple interest rate, than if she paid with cash?
Elizabeth's two payment options for purchasing a new item are shown in the table below:
| Purchase option | Interest rate (fixed) | Compounding interval | Payment interval |
|---|---|---|---|
| \text{Personal loan} | 7.45\% | \text{weekly} | \text{weekly} |
| \text{Hire purchase} | 6.85\% | \text{weekly} | \text{weekly} |
Which purchase option should Elizabeth choose in order to pay the least amount of interest?
Brad's two payment options for purchasing a new item are shown in the table below:
| Purchase option | Interest rate (fixed) | Compounding interval | Payment interval |
|---|---|---|---|
| \text{Personal loan} | 8.65\% | \text{weekly} | \text{quarterly} |
| \text{Hire purchase} | 8.65\% | \text{weekly} | \text{monthly} |
Do Brad's purchase options cost the same amount?
Luigi has two payment options for purchasing a new item as shown in the table below:
| Purchase option | Interest rate | Compounding interval |
|---|---|---|
| \text{Hire purchase} | 7.45\% | \text{quarterly} |
| \text{Personal loan} | 7.25\% | \text{monthly} |
Find the equivalent annual interest rate for the following purchase options to two decimal places:
Hire Purchase
Personal loan
What option should Luigi choose in order to pay the least interest? Assume that he pays in quarterly intervals.
The following purchase options were provided to a customer. Assume the payment intervals for each purchase option are the same:
| Purchase option | Interest rate | Compounding interval |
|---|---|---|
| \text{Credit card} | 6.85\% | \text{daily} |
| \text{Hire purchase} | 6.65\% | \text{weekly} |
Find the effective equivalent annual interest rate for the options to two decimal places:
Credit card
Hire purchase
Which option is the most affordable? Explain your answer.
The sale price of a television is \$581. Noah chooses to purchase the television on credit card, with 7 days interest free. His card has an interest rate of 26.75\% p.a., compounded daily.
Noah pays \$208 off on the day of purchase. How much does he still owe?
Noah wants to avoid paying more than \$610. How many full days, n, from the date of purchase does Noah have before the total costs exceed \$610?
Irene wants to buy a second hand car for \$1685 and is deciding between using her credit card or taking out a personal loan. The interest rates and additional fees for a credit card and a personal loan are shown in the table:
If Irene chooses to take out a personal loan, how much money will she spend in fees in the first year?
If Irene decides to apply for a credit card and pay with that, how much will she spend on fees in the first year?
| Personal Loan | Credit Card | |
|---|---|---|
| Legal fee | \$100 | \text{NA} |
| Application Fee | \$350 | \$200 |
| Annual Fee | \$30 | \$80 |
| Interest (p.a.) | 18.45\% | 17.75\% |
| Copounding interval | \text{Monthly} | \text{Daily} |
Irene takes a loan out for \$1685 and pays \$825 during each monthly payment interval (or the remaining balance if less than \$825). A record of the following payments and owing balance has been started in the following table:
| Balance (before interest) | Balance (after interest) | Payment | Balance (owing) | |
|---|---|---|---|---|
| \text{Month } 1 | \$1685 | \$1710.91 | \$825 | \$885.91 |
| \text{Month }2 | \$885.91 | |||
| \text{Month } 3 |
Complete the above table.
How much does Irene pay using a personal loan, including fees?
Consider the situation if Irene uses a credit card instead with 40 interest-free days. If she pays her balance within the interest free period, how much does she pay including fees?
A store offered interest free terms for 20 months on all purchases. Valentina purchased a \$220 treadmill by paying an initial \$37 deposit followed by 5 monthly instalments. If she was also charged an account keeping fee of \$5 per month, what is:
The size of each instalment?
The total amount paid for the treadmill?
Mae purchased a \$4084 sofa on a deferred payment plan. She paid a \$622 deposit, followed by nothing for the first year and then 33 fortnightly instalments of \$134.
How much did Mae pay for the sofa altogether?
How much interest did she pay?
What was the annual rate of interest charged for buying on a deferred payment plan? Round your answer to two decimal places.
Valentina received a loan of \$46\,700 that had to repaid, with interest of 5\% p.a., in 62 monthly instalments. Calculate the following:
The interest on the loan.
The total amount that had to be repaid.
The size of each monthly payment.
Neil bought a \$4800 LCD television on terms, and was given the choice of two payment plans :
-
Plan 1: 18\% deposit with 51 monthly instalments of \$212.
Plan 2: \$375 deposit and fortnightly instalments of \$52 over 6 years.
Which plan is most affordable for Neil? Support your answer with appropriate calculations.
Beth purchased a \$3200 second hand car on terms, and was given the choice of two payment plans:
Plan 1: 7\% deposit with monthly instalments of \$104 over 3 years.
Plan 2: \$362 deposit with 77 weekly instalments of \$63.
Which plan is most affordable for Beth? Support your answer with appropriate calculations.
Dave purchased a desk, valued at \$878, on interest free terms for 21 months, with an initial \$80 deposit and 9 monthly payments.
A penalty fee of 10\% of the balance owing is charged for instalments that are not paid on time.
Find the monthly instalment.
Find the penalty fee due if Dave is late in paying the third monthly instalment.
Han made the following purchases:
-
Item A: A fridge, valued at \$702, on terms. He paid a 6\% deposit, followed by monthly instalments of \$21 over 3 years.
Item B: A couch, valued at \$726, on terms. He paid a 11\% deposit, followed by fortnightly instalments of \$10 over 3 years.
Item C: A TV, valued at \$975, on terms. He paid a 12\% deposit, followed by weekly instalments of \$5 over 4 years.
Item D: A car, valued at \$36\,653, on a deferred payment plan. He paid a \$1714 deposit, followed by nothing for the first 6 months and then 31 monthly instalments of \$1266.
Complete the following table. Round your answers to two decimal places.
| Item A | Item B | Item C | Item D | |
|---|---|---|---|---|
| \text{Deposit paid for the item } (\$) | ||||
| \text{Balance owing (after deposit) } (\$) | ||||
| \text{Total payments in installment } (\$) | ||||
| \text{Total payment for the item } (\$) | ||||
| \text{Interest charged to the item } (\$) | ||||
| \text{Interest charged as a percentage to the item } (\%) | ||||
| \text{Annual rate of simple interest } (\%) |
Luigi purchased the following items:
Item A: Blu-ray player that retailed for \$598, on terms. He paid a 8\% deposit, followed by monthly instalments over 2 years, with simple interest charged on the balance at 10\% p.a.
Item B: A trailer, that cost \$54\,950, on terms. He paid a down payment of 14\% and weekly instalments over 14 years, with interest charged on the balance at 15\% p.a.
Item C: A table, priced at \$190, on terms. He paid a 8\% deposit and 34 fortnightly instalments, with interest charged on the balance at 14\% p.a.
Complete the following table. Round your answers to two decimal places.
| Item A | Item B | Item C | |
|---|---|---|---|
| \text{Deposit paid for the item } (\$) | |||
| \text{Balance owing (after deposit) } (\$) | |||
| \text{Total interest paid } (\$) | |||
| \text{Total amount of installments } (\$) | |||
| \text{Size of each installment } (\$) | |||
| \text{Total payment for the item } (\$) | |||
| \text{Interest charged as percentage of the cost of the item } (\%) |