IB · Mathematics: Applications & Interpretation SL & HL · Number & algebra

Financial mathematics: IB Mathematics: Applications & Interpretation questions with answers

Free Financial mathematics questions for IB Mathematics: Applications & Interpretation (SL & HL), part of Number & algebra. Each question has the answer and the marking points an examiner would look for.

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Financial mathematics practice questions

Question 1Structured · 6 marksA* challenge

Lena has $200000 in a retirement account earning 4.2% per year, compounded monthly. She withdraws $1200 at the end of each month.

(a)

Find the number of complete months for which she can make the full withdrawal.

[3]
(b)

Find the monthly withdrawal that would make the money last exactly 25 years.

[3]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)250 months
TVM: PV = −200000, PMT = 1200, FV = 0, I% = 4.2 (M1)(A1)
250 months A1
3
(b)$1077.88
N = 300, FV = 0 (M1)
solving for PMT (M1)
$1077.88 A1
3
Question 2Structured · 5 marks

A car is bought for $45000. Its value depreciates by 18% each year.

(a)

Find the value of the car after 4 years.

[2]
(b)

Find the number of complete years after which the car is first worth less than half its original price.

[3]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)$20345
45000(0.82)4 (M1)
$20345 A1
2
(b)4 years
45000(0.82)n < 22500 (M1)
attempt to solve, e.g. table or logs (M1)
4 A1
3
Question 3Structured · 7 marks

Kai takes out a loan of $250000 at a nominal annual interest rate of 6.4%, compounded monthly. The loan is repaid with equal monthly payments over 25 years.

(a)

Find the monthly payment.

[3]
(b)

Find the total interest paid.

[2]
(c)

Find the amount still owed after 13 years.

[2]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)$1672.43
N = 300, I% = 6.4, PV = 250000, FV = 0, P/Y = C/Y = 12 (M1)(A1)
$1672.43 A1
3
(b)$251728.91
300 × 1672.43 − 250000 (M1)
$251728.91 A1
2
(c)$167800.80
TVM with N = 156, solving for FV (M1)
$167800.80 A1
2
Question 4Structured · 14 marksA* challenge

Sara invests $20000 at 4% per year compounded annually. Inflation is 3% per year.

(a)

Find the value of the investment after 15 years.

[2]
(b)

Find the real value of the investment after this time.

[3]
(c)

Instead, Sara saves $300 at the end of each month at 4% per year compounded monthly. Find the value after 15 years.

[3]
(d)

Find the monthly saving needed to reach $36000 in 15 years under the monthly plan.

[3]
(e)

Compare the two plans, considering the total amount invested.

[3]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)$36018.87
TVM or formula (M1)
$36018.87 A1
2
(b)$23219.38
real rate 1% (A1)
TVM with the real rate (M1)
$23219.38 A1
3
(c)$73827.15
N = 180, PMT = −300, PV = 0 (M1)(A1)
$73827.15 A1
3
(d)$146.29
FV = 36000 (M1)
solving for PMT (M1)
$146.29 A1
3
(e)comparison
plan 1 invests $20000 A1
plan 2 invests $54000.00 A1
valid comparison with reason R1
3
Question 5Structured · 6 marksA* challenge

Lena has $150000 in a retirement account earning 3% per year, compounded monthly. She withdraws $1500 at the end of each month.

(a)

Find the number of complete months for which she can make the full withdrawal.

[3]
(b)

Find the monthly withdrawal that would make the money last exactly 25 years.

[3]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)115 months
TVM: PV = −150000, PMT = 1500, FV = 0, I% = 3 (M1)(A1)
115 months A1
3
(b)$711.32
N = 300, FV = 0 (M1)
solving for PMT (M1)
$711.32 A1
3
Question 6Structured · 6 marks

Ana invests $5000 in an account that pays a nominal annual interest rate of 2.5%, compounded monthly.

(a)

Find the value of the investment after 5 years, to the nearest dollar.

[3]
(b)

Find the number of complete years needed for the investment to exceed $7500.

[3]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)$5665
N = 60, I% = 2.5, PV = −5000, P/Y = C/Y = 12 (M1)(A1)
$5665 A1
3
(b)17 years
FV = 7500, solve for N (M1)
N = 195 (A1)
17 years A1
3

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Original IB-style practice questions written for mentorriyaz.in. These are not IB past paper questions, and this site is not affiliated with or endorsed by the International Baccalaureate Organization. Updated 2026-11-04. Paper generator · mentorriyaz.in