James borrows \$75\,000 at a rate of 3.5\% (per annum) reducible interest compounded quarterly. At the end of each quarter he makes a repayment of \$2100.
Using the financial application on the CAS calculator:
Which variable do we want to solve for if we wish to determine the length of the loan?
State the value of:
\text{I}\%
\text{PV}
\text{Pmt}
\text{FV}
\text{PpY}
\text{CpY}
Hence, find after how many quarters the loan will be repaid.
Mr and Mrs Gwen held a mortgage for 25 years. Over that time they made monthly repayments of \$4500 and were charge a fixed interest rate of 4.4\% per annum, compounded monthly.
Complete the given table, leaving out the unknown variable.
Hence, use the financial application on your CAS calculator to determine how much Mr. and Mrs. Gwen initially borrowed.
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Ben borrows \$25\,000 to buy a car. He is charged 4.8\% reducible interest compounded monthly.
Use the financial application on your CAS calculator to determine what his monthly repayments will be if he wishes to pay off the loan in 5 years.
Molly borrows \$65\,000 and is charged quarterly reducible interest at a rate of 4.5\% per annum compounded quarterly.
Use the financial application on your CAS calculator to determine what her quarterly repayments should be if she wishes to pay off the loan in 7 years.
Aaron borrows \$15\,000 to buy a car. He is charged 6.8\% reducible interest compounded monthly. He wishes to pay off the loan in 3 years.
Complete the given table, leaving out the unknown variable.
Hence, use the financial application on your CAS calculator to find the minimum value of his monthly repayments.
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| CpY |
Derek borrows \$50\,000 at a rate of 9\% (per annum) reducible interest compounded quarterly. At the end of each quarter he makes a repayment of \$1800.
Complete the given table, leaving out the unknown variable.
Hence, use the financial application on your CAS calculator to find how many quarters it will take for the loan to be repaid.
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| I\% | |
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| CpY |
Tom has a mortgage of \$500\,000 reducible monthly with an annual interest rate of 4.2\%. He makes fortnightly repayments of \$1500. Assume that there are 26 fortnights in a year.
Complete the given table, leaving out the unknown variable.
Hence state the number of full years it will take to pay off the loan.
If Tom would like to pay off his loan in 10 years, find the fortnightly repayment he needs to make, to the nearest dollar.
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Pauline and Brad borrow \$330\,000 for a house extension. The bank offers them 2.75\% p.a compounded daily. They also make a payment of \$67 per day. Assume there are 365 days in a year.
Complete the given table.
Determine the whole number of years it will take until Pauline and Brad pay back the \$330\,000 loan required for the extension.
If they change their payment to \$75 per day, how many whole years will it take until they pay the loan?
How many years do they save by increasing their payment to \$75?
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| N | - |
| I\% | |
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| P/Y | |
| C/Y |
Valentina is deciding between two \$109\,000 home loans. She has the capacity to pay \$3400 per month.
Option 1: 3.2\% p.a. over 3 years with fixed monthly repayments.
Option 2: 2.6\% p.a. over 3 years with minimum monthly repayments of \$3151 that enables paying more than the minimum monthly repayment
What are the fixed monthly repayments she will have to make with Option 1?
What is the total repayment she will have to make with Option 1?
What is the maximum total repayment she will have to make with Option 2?
Which loan will cost Valentina less?
Sue borrows \$42\,000 at a rate of 4.1\% (per annum) reducible interest compounded monthly. At the end of each month she makes a repayment of \$480
Which variable do we want to solve for if we wish to determine the length of the loan?
State the value of:
\text{I}\%
\text{PV}
\text{Pmt}
\text{FV}
\text{PpY}
\text{CpY}
Hence, state after how many months the loan will be repaid.
Calculate the amount of the final payment.
Calculate the total amount Sue paid.
Calculate how much Sue paid in interest.
Xanthe borrows \$32\,000 at a rate of 6.5\% (per annum) reducible interest compounded monthly. At the end of each month she makes a repayment of \$380.
Complete the given table, leaving out the unknown variable.
Hence, use the financial application on your CAS calculator to determine how many months it will take for the loan to be repaid.
Calculate the total amount Xanthe paid.
Calculate how much Xanthe paid in interest.
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| CpY |
Tara borrows \$15\,000 and is charged quarterly reducible interest at a rate of 7\% per annum compounded quarterly. She wishes to pay off the loan in 7 years.
Complete the given table, leaving out the unknown variable.
Hence, use the financial application on your CAS calculator to determine the minimum value of her quarterly repayments.
Calculate the total amount Tara paid.
Calculate how much Tara paid in interest.
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Fred borrows \$9800 for a skiing holiday. The bank offers a personal loan at 2.25\% p.a compounded monthly. He will make a monthly payment of \$200.
Complete the given table.
Determine the number of whole months it will take until Fred is able to pay the \$9800 loan.
Determine the balance after 51 months.
Calculate the monthly interest rate.
Hence determine the amount of the final payment, including the interest.
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Caitlin borrows \$250\,000 to buy a unit and wants to pay it back before she is 33. She just turned 23 years old and the current interest rate is 3.2\% p.a. compounded monthly. She wishes to find the monthly payment needed to reach her goal.
Complete the given table.
Determine the monthly payment required for Caitlin to repay the \$250\,000 loan by the time she is 33 years old.
How much does she pay in total over the term of the loan?
If she extends the term of the loan to 25 years, how much will her monthly payment be?
How much does she pay in total over the 25 years?
Hence, determine much money she saves if she pays the loan back after 10 years instead of 25 years.
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| I\% | |
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| Pmt | - |
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| C/Y |
Pauline and Jenny take out a loan of \$120\,000 for a new caravan. The loan rate is 3.015\% p.a compounded weekly. They decide to make payments of \$100 per week. Assume there are 52 weeks in a year.
Complete the given table.
Determine the whole number of weeks it will take until Pauline and Jenny pay back the \$120\,000 loan they borrowed for the caravan.
Assuming all payments are equal in size, how much do Pauline and Jenny pay for the caravan?
If they decide to triple their payment to \$300 per week, how many whole weeks will it take them until they pay the loan?
Hence, calculate how much money they save if they triple their payment.
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An entrepreneur borrows \$1\,200\,000 from a bank at an interest of 1.85\% p.a. compounded weekly and makes \$5000 per week payments into the loan account. Assume there are 52 weeks in a year.
Complete the given table.
Determine the whole number of weeks it will take until the entrepreneur pays off their loan.
Calculate the amount of the final payment of the loan.
Hence determine the total amount the entrepreneur pays over the duration of the loan.
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A business man borrows \$235\,000 from a bank offering a rate of 2.85\% compounded daily. He also makes \$100 per day payments into the account. Assume there are 365 days in a year.
Complete the given table.
Determine the whole number of days it will take until the business man pays off their loan.
Calculate the amount of the final payment of the loan.
Hence calculate how much the businessman pays over the duration of the loan.
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| I\% | |
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| FV | |
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| C/Y |
A student borrows \$60\,000 to pay their student loan. The bank offers a reducing balance loan and charges a student rate of 0.95\% p.a. compounded weekly. She wants to pay the loan off completely in 8 years in equal monthly payments. Assume there are 52 weeks in a year.
Complete the given table.
State the monthly payment required.
How much should she pay each month if she wants to pay the loan off in half the time?
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| Pmt | - |
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A young couple wish to borrow \$210\,000.
Bank 1 is advertising a reducing balance loan with an interest rate of 3.05\% p.a. compounded monthly and quarterly payments of \$5000.
Bank 2 offers them the deal that they can pay the loan in 60 installments of \$4500.
Complete the given table for Bank 1.
Calculate the number of whole quarters it takes until the loan is paid using Bank 1.
Calculate the total amount paid to Bank 2 over the duration of the loan.
Which bank should the couple choose? Explain your answer.
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Stephen borrows \$12\,500 to buy a car. The bank offers a reducing balance loan with interest rate of 4.6\% p.a. compounded monthly. Stephen chooses to make weekly payments of \$100 in order to pay off the loan. Assume there are 52 weeks in a year.
What is the balance of the loan after 20 weeks?
How long does it take him to pay off the loan in years? Round your answers to two decimal places.
Kate borrows \$14\,800 to buy a car. The bank offers a reducing balance loan with an interest rate of 3.5\% p.a. compounded monthly. Kate chooses to make weekly payments of \$90 in order to pay off the loan.
What is the balance after 52 weeks?
How long does it take her to pay off the loan in years? Round your answers to two decimal places.
Valerie borrows \$345\,000 to buy an apartment. The bank offers a reducing balance loan with an interest rate of 2.35\% p.a. compounded monthly. Valerie chooses to make fortnightly payments of \$1250 in order to pay off the loan. Use the financial application on your calculator to answer the following questions. Assume there are 26 fortnights in a year.
What is the balance after 100 weeks?
How long does it take her to pay off the loan in years? Round your answers to two decimal places.