SL 1.7—Loan repayments and amortization Questionbank

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.

Paper

Level

Question 1

SLPaper 2

Terrence has $800000$ in his savings fund. He rolls his money into an annuity fund which earns $4.7 \%$ compounded monthly. He wants to withdraw $7000$ each month to live on.

How long will his money last.

[2]

How much longer would his money last if he only withdrew $6000$ each month.

[3]

Question 2

SLPaper 2

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 $15 \%$ , compounded monthly. No deposit required and repayments are made each month.

Find the repayment made each month.

[2]

Question 3

SLPaper 2

Phillip takes out a loan of $ 47000. The unpaid balance on the loan has an interest rate of $4.97 \%$ , 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.

[3]

After 1.5 years, Phillip misses a payment. The penalty for missing a payment is $5.5 \%$ of the remaining balance. Calculate the total amount paid for the loan.

[6]

Question 4

SLPaper 2

A 5 year loan of $\$ 20000 $at a nominal annual interest rate of$ r % $compounded quarterly. Terms of the loan require a$ 5 % $deposit and a monthly repayment of$ $ 400$.

Find the annual interest rate, $r$ .

[4]

Question 5

SLPaper 2

Jimmy has been renting out his apartment for $\$ 1200 $per month, however he wants to renovate the apartment to increase the monthly rent to$ $ 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.

[1]

Jimmy takes out a loan of $\$ 25000 $to renovate the apartment. Terms of the loan are : A nominal annual interest rate of$ 6.2 % $, compounded monthly Monthly repayments of$ $ 850$. Calculate the total amount paid for the renovations.

[3]

Question 6

SLPaper 2

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 $12 \%$ nominal annual interest rate, compounded quarterly, a 15% deposit and repayments to be made each quarter .

Calculate the loan amount John would receive.

[3]

Question 7

SLPaper 2

Sushi takes out a loan of $\$ 19800 $to purchase new tools for his gardening business. She agrees to pay the bank$ $ 840 $at the end of every quarter to amortise the loan. The loan has a nominal annual interest rate of$ 4.34 %$ per year, compounding semi-annually.

Find out how long it takes to pay back the loan.

[3]

Question 8

SLPaper 2

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.

[3]

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.

[3]

Question 9

SLPaper 2

In this question, give all answers to two decimal places.

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 $r$ % compounded monthly. Terms of the loan require a 10% deposit and monthly repayments of €250.

State which option Bryan should choose. Justify your answer.

[2]

Find the amount to be borrowed for this option.

[2]

Find the annual interest rate, $r$ .

[3]

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.

[3]

Find the total amount paid for the car.

[2]

Find the interest paid on the loan.

[2]

Find the repayment made each quarter.

[3]

Question 10

SLPaper 1

Sophia pays $$ 200$ into a bank account at the end of each month. The annual interest paid onmoney 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.

[3]

Find an approximation for the real interest rate for the money invested in theaccount.

[2]

Hence find the real value of Sophia’s investment at the end of $5$ years.

[2]