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.
Terrence has in his savings fund. He rolls his money into an annuity fund which earns compounded monthly. He wants to withdraw each month to live on.
How long will his money last.
How much longer would his money last if he only withdrew each month.
Cary decides to buy a new boat at a cost of \ 20000$, but cannot afford the full amount. The boat dealership offers him to finance a loan.
A 5 year loan at a nominal annual interest rate of , compounded monthly. No deposit required and repayments are made each month.
Find the repayment made each month.
Phillip takes out a loan of $ 47000. The unpaid balance on the loan has an interest rate of , compounded semi-annually. The loan is to be repaid in payments of $ 2120 at the end of every quarter.
Calculate the number of years it will take to repay the loan.
After 1.5 years, Phillip misses a payment. The penalty for missing a payment is of the remaining balance. Calculate the total amount paid for the loan.
A 5 year loan of \ 20000r %5 %$ 400$.
Find the annual interest rate, .
Jimmy has been renting out his apartment for \ 1200$ 1750$. He notifies his current tenants and they agree to move out. The renovations are expected to take 5 months.
Calculate the amount of rental income Aaron is foregoing by deciding to renovate the apartment.
Jimmy takes out a loan of \ 250006.2 %$ 850$. Calculate the total amount paid for the renovations.
John decides to purchase a new van from a dealership which costs \ 18000$, which 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 15% deposit and repayments to be made each quarter .
Calculate the loan amount John would receive.
Sushi takes out a loan of \ 19800$ 8404.34 %$ per year, compounding semi-annually.
Find out how long it takes to pay back the loan.
Peter is looking at two homes for his family to move into. The first home is located out of town and is listed at \ 775000$ 620000$.
The bank offers Peter an identical loan for both homes. Terms of the loan are: 20% deposit nominal annual interest rate, compounded quarterly Repayments of to be paid at the end of every month.
Calculate the loan amount for the :
First home
Second home
Find the number of months and years to pay off the loan for the : First home
Second home
Luke rolls his of savings into an annuity fund which earns interest compounded monthly. He wants the money to last for 16 years.
How much money can Luke withdraw each month?
Find the outstanding balance of the fund after 10 years.
Henry has retired at age 68 with \ 8300004 %$ 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 per month. Will Henry be able to maintain his current standard of living? Explain your answer.