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.
Give your answers in this question correct to the nearest whole number.
Imon invested $25\,000$ Singapore dollars (SGD) in a fixed deposit account with a nominal annual interest rate of $3.6\%$, compounded monthly.
Calculate the value of Imon’s investment after $5$ years.
At the end of the $5$ years, Imon withdrew $x$ SGD from the fixed deposit account and reinvested this into a super-savings account with a nominal annual interest rate of $5.7\%$, compounded half-yearly.
The value of the super-savings account increased to $20\,000$ SGD after $18$ months.
Find the value of $x$.
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.
Sophia pays \$200 into a bank account at the end of each month. The annual interest paid on money in the account is $3.1\%$ which is compounded monthly.
The average rate of inflation per year over the 5 years was $2\%$.
Find the value of her investment after a period of 5 years.
Find an approximation for the real interest rate for the money invested in the account.
Calculate the real value of Sophia’s investment at the end of 5 years.
Give your answers to parts 2, 3 and 4 to the nearest whole number.
Harinder has 14 000 US Dollars (USD) to invest for a period of five years. He has two options of how to invest the money.
Option A: Invest the full amount, in USD, in a fixed deposit account in an American bank.
The account pays a nominal annual interest rate of r% , compounded yearly, for the five years. The bank manager says that this will give Harinder a return of 17 500 USD.
Option B: Invest the full amount, in Indian Rupees (INR), in a fixed deposit account in an Indian bank. The money must be converted from USD to INR before it is invested.
The exchange rate is 1 USD = 66.91 INR.
The account in the Indian bank pays a nominal annual interest rate of 5.2 % compounded monthly.
Calculate the value of r.
Calculate 14 000 USD in INR.
Calculate the amount of this investment, in INR, in this account after five years.
Harinder chose option B. At the end of five years, Harinder converted this investment back to USD. The exchange rate, at that time, was 1 USD = 67.16 INR.
Calculate how much more money, in USD, Harinder earned by choosing option B instead of option A.
Juliana plans to invest money for 10 years in an account paying 3.5% interest, compounded annually. She expects the annual inflation rate to be 2% per year throughout the 10-year period. Juliana would like her investment to be worth a real value of €4000, compared to current values, at the end of the 10-year period. She is considering two options.
For option 1, determine the minimum amount Juliana would need to invest. Give your answer to the nearest euro.
For option 2, find the minimum value of that Juliana would need to invest each year. Give your answer to the nearest euro.
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 .
Phil takes out a bank loan of $\$150\,000$ to buy a house, at an annual interest rate of $3.5\%$. The interest is calculated at the end of each year and added to the amount outstanding.
To pay off the loan, Phil makes annual deposits of $\$P$ at the end of every year in a savings account, paying an annual interest rate of $2\%$. He makes his first deposit at the end of the first year after taking out the loan.
David visits a different bank and makes a single deposit of $\$Q$, the annual interest rate being $2.8\%$.
Find the amount Phil would owe the bank after 20 years. Give your answer to the nearest dollar.
Show that the total value of Phil’s savings after 20 years is $$\frac{(1.02^{20} - 1)P}{1.02 - 1}$$
Given that Phil’s aim is to own the house after 20 years, find the value for $P$ to the nearest dollar.
David wishes to withdraw $\$5000$ at the end of each year for a period of $n$ years. Show that an expression for the minimum value of $Q$ is
$$ \frac{5000}{1.028} + \frac{5000}{1.028^2} + \dots + \frac{5000}{1.028^n} $$
Hence or otherwise, find the minimum value of $Q$ that would permit David to withdraw annual amounts of $\$5000$ indefinitely. Give your answer to the nearest dollar.
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.
Give your answers in this question correct to the nearest whole number.
Imon invested $25\,000$ Singapore dollars (SGD) in a fixed deposit account with a nominal annual interest rate of $3.6\%$, compounded monthly.
Calculate the value of Imon’s investment after $5$ years.
At the end of the $5$ years, Imon withdrew $x$ SGD from the fixed deposit account and reinvested this into a super-savings account with a nominal annual interest rate of $5.7\%$, compounded half-yearly.
The value of the super-savings account increased to $20\,000$ SGD after $18$ months.
Find the value of $x$.
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.
Sophia pays \$200 into a bank account at the end of each month. The annual interest paid on money in the account is $3.1\%$ which is compounded monthly.
The average rate of inflation per year over the 5 years was $2\%$.
Find the value of her investment after a period of 5 years.
Find an approximation for the real interest rate for the money invested in the account.
Calculate the real value of Sophia’s investment at the end of 5 years.
Give your answers to parts 2, 3 and 4 to the nearest whole number.
Harinder has 14 000 US Dollars (USD) to invest for a period of five years. He has two options of how to invest the money.
Option A: Invest the full amount, in USD, in a fixed deposit account in an American bank.
The account pays a nominal annual interest rate of r% , compounded yearly, for the five years. The bank manager says that this will give Harinder a return of 17 500 USD.
Option B: Invest the full amount, in Indian Rupees (INR), in a fixed deposit account in an Indian bank. The money must be converted from USD to INR before it is invested.
The exchange rate is 1 USD = 66.91 INR.
The account in the Indian bank pays a nominal annual interest rate of 5.2 % compounded monthly.
Calculate the value of r.
Calculate 14 000 USD in INR.
Calculate the amount of this investment, in INR, in this account after five years.
Harinder chose option B. At the end of five years, Harinder converted this investment back to USD. The exchange rate, at that time, was 1 USD = 67.16 INR.
Calculate how much more money, in USD, Harinder earned by choosing option B instead of option A.
Juliana plans to invest money for 10 years in an account paying 3.5% interest, compounded annually. She expects the annual inflation rate to be 2% per year throughout the 10-year period. Juliana would like her investment to be worth a real value of €4000, compared to current values, at the end of the 10-year period. She is considering two options.
For option 1, determine the minimum amount Juliana would need to invest. Give your answer to the nearest euro.
For option 2, find the minimum value of that Juliana would need to invest each year. Give your answer to the nearest euro.
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 .
Phil takes out a bank loan of $\$150\,000$ to buy a house, at an annual interest rate of $3.5\%$. The interest is calculated at the end of each year and added to the amount outstanding.
To pay off the loan, Phil makes annual deposits of $\$P$ at the end of every year in a savings account, paying an annual interest rate of $2\%$. He makes his first deposit at the end of the first year after taking out the loan.
David visits a different bank and makes a single deposit of $\$Q$, the annual interest rate being $2.8\%$.
Find the amount Phil would owe the bank after 20 years. Give your answer to the nearest dollar.
Show that the total value of Phil’s savings after 20 years is $$\frac{(1.02^{20} - 1)P}{1.02 - 1}$$
Given that Phil’s aim is to own the house after 20 years, find the value for $P$ to the nearest dollar.
David wishes to withdraw $\$5000$ at the end of each year for a period of $n$ years. Show that an expression for the minimum value of $Q$ is
$$ \frac{5000}{1.028} + \frac{5000}{1.028^2} + \dots + \frac{5000}{1.028^n} $$
Hence or otherwise, find the minimum value of $Q$ that would permit David to withdraw annual amounts of $\$5000$ indefinitely. Give your answer to the nearest dollar.