Practice SL 1.4—Financial apps – compound interest, annual depreciation 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.
A car depreciates in value exponentially. The initial value of the car is $20,000, and it depreciates at a rate of 15% per year.
Calculate the value of the car after 5 years.
Determine the time it takes for the car's value to halve.
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.
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.
Tommaso and Pietro have each been given 1500 euro to save for college. Pietro invests his money in an account that pays a nominal annual interest rate of 2.75%, compounded half-yearly. Tommaso wants to invest his money in an account such that his investment will increase to 1.5 times the initial amount in 5 years. Assume the account pays a nominal annual interest of % compounded quarterly.
Calculate the amount Pietro will have in his account after 5 years. Give your answer correct to 2 decimal places.
Determine the value of .
On the day of her birth, 1st January 1998, Mary's grandparents invested in a savings account. They continued to deposit on the first day of each month thereafter.
The account paid a fixed rate of interest per month. The interest was calculated on the last day of each month and added to the account.
Let be the amount in Mary's account on the last day of the th month, immediately after the interest had been added.
Find an expression for and show that .
(i) Write down a similar expression for and .
(ii) Hence show that the amount in Mary's account the day before she turned 10 years old is given by .
Write down an expression for in terms of on the day before Mary turned 18 years old showing clearly the value of .
Mary's grandparents wished for the amount in her account to be at least the day before she was 18. Determine the minimum value of the monthly deposit required to achieve this. Give your answer correct to the nearest dollar.
As soon as Mary was 18 she decided to invest of this money in an account of the same type earning interest per month. She withdraws every year on her birthday to buy herself a present. Determine how long it will take until there is no money in the account.
Give your answers to this question correct to two decimal places.
Gen invests $2400 in a savings account that pays interest at a rate of 4% per year, compounded annually. She leaves the money in her account for 10 years, and she does not invest or withdraw any money during this time.
Calculate the value of her savings after 10 years.
The rate of inflation during this 10 year period is 1.5% per year.
Calculate the real value of her savings after 10 years.
Practice SL 1.4—Financial apps – compound interest, annual depreciation 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.
A car depreciates in value exponentially. The initial value of the car is $20,000, and it depreciates at a rate of 15% per year.
Calculate the value of the car after 5 years.
Determine the time it takes for the car's value to halve.
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.
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.
Tommaso and Pietro have each been given 1500 euro to save for college. Pietro invests his money in an account that pays a nominal annual interest rate of 2.75%, compounded half-yearly. Tommaso wants to invest his money in an account such that his investment will increase to 1.5 times the initial amount in 5 years. Assume the account pays a nominal annual interest of % compounded quarterly.
Calculate the amount Pietro will have in his account after 5 years. Give your answer correct to 2 decimal places.
Determine the value of .
On the day of her birth, 1st January 1998, Mary's grandparents invested in a savings account. They continued to deposit on the first day of each month thereafter.
The account paid a fixed rate of interest per month. The interest was calculated on the last day of each month and added to the account.
Let be the amount in Mary's account on the last day of the th month, immediately after the interest had been added.
Find an expression for and show that .
(i) Write down a similar expression for and .
(ii) Hence show that the amount in Mary's account the day before she turned 10 years old is given by .
Write down an expression for in terms of on the day before Mary turned 18 years old showing clearly the value of .
Mary's grandparents wished for the amount in her account to be at least the day before she was 18. Determine the minimum value of the monthly deposit required to achieve this. Give your answer correct to the nearest dollar.
As soon as Mary was 18 she decided to invest of this money in an account of the same type earning interest per month. She withdraws every year on her birthday to buy herself a present. Determine how long it will take until there is no money in the account.
Give your answers to this question correct to two decimal places.
Gen invests $2400 in a savings account that pays interest at a rate of 4% per year, compounded annually. She leaves the money in her account for 10 years, and she does not invest or withdraw any money during this time.
Calculate the value of her savings after 10 years.
The rate of inflation during this 10 year period is 1.5% per year.
Calculate the real value of her savings after 10 years.