Practice SL 1.7—Loan repayments and amortization with authentic IB Mathematics Applications & Interpretation (AI) exam questions for both SL and HL students. This question bank mirrors Paper 1, 2, 3 structure, covering key topics like core principles, advanced applications, and practical problem-solving. Get instant solutions, detailed explanations, and build exam confidence with questions in the style of IB examiners.
Yejin plans to retire at age 60. She wants to create an annuity fund, which will pay her a monthly allowance of $4000 at the end of each month during her retirement. She wants to save enough money so that the payments last for 30 years. A financial advisor has told her that she can expect to earn 5% interest on her funds, compounded annually.
Calculate the amount Yejin needs to have saved into her annuity fund, in order to meet her retirement goal. Give your answer to the nearest dollar.
Yejin has just turned 28 years old. She currently has no retirement savings. She wants to save part of her salary at the end of each month into her annuity fund.
Calculate the amount Yejin needs to save each month, to meet her retirement goal given the same annual interest and annual compounding. Give your answer to the nearest dollar.
Terrence has $800,000 in his savings fund. He rolls his money into an annuity fund which earns compounded monthly. He wants to withdraw $7000 each month to live on.
How long will his money last?
How much longer would his money last if he only withdrew $6000 each month?
Cary decides to buy a new boat at a cost of $20,000, but cannot afford the full amount. The boat dealership offers a financing plan.
A 5-year loan at a nominal annual interest rate of , compounded monthly. No deposit is required and repayments are made each month.
Find the repayment made each month.
Bryan decides to purchase a new car with a price of €14 000, but cannot afford the full amount. The car dealership offers two options to finance a loan.
Finance option A:
A 6 year loan at a nominal annual interest rate of 14% compounded quarterly. No deposit required and repayments are made each quarter.
Finance option B:
A 6 year loan at a nominal annual interest rate of % compounded monthly. Terms of the loan require a 10% deposit and monthly repayments of €250.
In this question, give all answers to two decimal places.
Find the repayment made each quarter for Option A.
Find the total amount paid for the car under Option A.
Find the interest paid on the loan for Option A.
Find the amount to be borrowed for Option B.
Find the annual interest rate, .
State which option Bryan should choose. Justify your answer.
Bryan's car depreciates at an annual rate of 25% per year.
Find the value of Bryan's car six years after it is purchased.
John decides to purchase a new van from a dealership which costs , but he cannot afford to pay the full amount.
The dealership offers him a finance option in the form of a 4-year loan. Terms of the loan are a nominal annual interest rate, compounded quarterly, a deposit and repayments to be made each quarter.
Calculate the loan amount John would receive.
In this question, give all answers correct to 2 decimal places. Raul and Rosy want to buy a new house and they need a loan of 170000 Australian dollars (AUD) from a bank. The loan is for 30 years and the annual interest rate for the loan is 3.8%, compounded monthly. They will pay the loan in fixed monthly instalments at the end of each month.
Find the amount they will pay the bank each month.
Find the amount Raul and Rosy will still owe the bank at the end of the first 10 years.
Using your answers to Part 1 and Part 2, calculate how much interest they will have paid in total during the first 10 years.
Peter is looking at two homes for his family to move into. The first home is located out of town and is listed at and the second home is located in town and is listed at .
The bank offers Peter an identical loan for both homes. The terms of the loan are:
Calculate the loan amount for the:
First home
Second home
Find the number of months and years to pay off the loan for the first home.
Find the number of months and years to pay off the loan for the second home.
Luke rolls his $700,000 of savings into an annuity fund which earns interest compounded monthly. He wants the money to last for 16 years.
How much money can Luke withdraw each month?
Find the outstanding balance of the fund after 10 years.
Henry has retired at age 68 with $830,000 in his savings fund. He rolls the money into an annuity fund which earns compounded monthly.
If Henry wants the money to last until he is 85, how much can he afford to withdraw each month?
Henry currently lives on $6000 per month. Will Henry be able to maintain his current standard of living? Explain your answer.
Lucy takes a mortgage of $ to purchase a house at a nominal annual interest rate of , compounded monthly. She agrees to pay the bank $ at the end of every month to amortise the loan. Find:
The number of years and months it will take Lucy to pay back the loan.
Practice SL 1.7—Loan repayments and amortization with authentic IB Mathematics Applications & Interpretation (AI) exam questions for both SL and HL students. This question bank mirrors Paper 1, 2, 3 structure, covering key topics like core principles, advanced applications, and practical problem-solving. Get instant solutions, detailed explanations, and build exam confidence with questions in the style of IB examiners.
Yejin plans to retire at age 60. She wants to create an annuity fund, which will pay her a monthly allowance of $4000 at the end of each month during her retirement. She wants to save enough money so that the payments last for 30 years. A financial advisor has told her that she can expect to earn 5% interest on her funds, compounded annually.
Calculate the amount Yejin needs to have saved into her annuity fund, in order to meet her retirement goal. Give your answer to the nearest dollar.
Yejin has just turned 28 years old. She currently has no retirement savings. She wants to save part of her salary at the end of each month into her annuity fund.
Calculate the amount Yejin needs to save each month, to meet her retirement goal given the same annual interest and annual compounding. Give your answer to the nearest dollar.
Terrence has $800,000 in his savings fund. He rolls his money into an annuity fund which earns compounded monthly. He wants to withdraw $7000 each month to live on.
How long will his money last?
How much longer would his money last if he only withdrew $6000 each month?
Cary decides to buy a new boat at a cost of $20,000, but cannot afford the full amount. The boat dealership offers a financing plan.
A 5-year loan at a nominal annual interest rate of , compounded monthly. No deposit is required and repayments are made each month.
Find the repayment made each month.
Bryan decides to purchase a new car with a price of €14 000, but cannot afford the full amount. The car dealership offers two options to finance a loan.
Finance option A:
A 6 year loan at a nominal annual interest rate of 14% compounded quarterly. No deposit required and repayments are made each quarter.
Finance option B:
A 6 year loan at a nominal annual interest rate of % compounded monthly. Terms of the loan require a 10% deposit and monthly repayments of €250.
In this question, give all answers to two decimal places.
Find the repayment made each quarter for Option A.
Find the total amount paid for the car under Option A.
Find the interest paid on the loan for Option A.
Find the amount to be borrowed for Option B.
Find the annual interest rate, .
State which option Bryan should choose. Justify your answer.
Bryan's car depreciates at an annual rate of 25% per year.
Find the value of Bryan's car six years after it is purchased.
John decides to purchase a new van from a dealership which costs , but he cannot afford to pay the full amount.
The dealership offers him a finance option in the form of a 4-year loan. Terms of the loan are a nominal annual interest rate, compounded quarterly, a deposit and repayments to be made each quarter.
Calculate the loan amount John would receive.
In this question, give all answers correct to 2 decimal places. Raul and Rosy want to buy a new house and they need a loan of 170000 Australian dollars (AUD) from a bank. The loan is for 30 years and the annual interest rate for the loan is 3.8%, compounded monthly. They will pay the loan in fixed monthly instalments at the end of each month.
Find the amount they will pay the bank each month.
Find the amount Raul and Rosy will still owe the bank at the end of the first 10 years.
Using your answers to Part 1 and Part 2, calculate how much interest they will have paid in total during the first 10 years.
Peter is looking at two homes for his family to move into. The first home is located out of town and is listed at and the second home is located in town and is listed at .
The bank offers Peter an identical loan for both homes. The terms of the loan are:
Calculate the loan amount for the:
First home
Second home
Find the number of months and years to pay off the loan for the first home.
Find the number of months and years to pay off the loan for the second home.
Luke rolls his $700,000 of savings into an annuity fund which earns interest compounded monthly. He wants the money to last for 16 years.
How much money can Luke withdraw each month?
Find the outstanding balance of the fund after 10 years.
Henry has retired at age 68 with $830,000 in his savings fund. He rolls the money into an annuity fund which earns compounded monthly.
If Henry wants the money to last until he is 85, how much can he afford to withdraw each month?
Henry currently lives on $6000 per month. Will Henry be able to maintain his current standard of living? Explain your answer.
Lucy takes a mortgage of $ to purchase a house at a nominal annual interest rate of , compounded monthly. She agrees to pay the bank $ at the end of every month to amortise the loan. Find:
The number of years and months it will take Lucy to pay back the loan.