36 exam-style questions on Amortization and annuities using technology — topic 1.7 of Number and Algebra in the IB Mathematics: Applications and Interpretation syllabus — with answers and explanations. Samples below; the full set is free with an account.
Maya takes out a mortgage of $250,000 at a nominal annual interest rate of 4.2%, compounded monthly, to be repaid with equal monthly payments over 25 years. Calculate the monthly repayment, to the nearest dollar.
Answer: $1347
Using the TVM solver with N = 300, I% = 4.2, PV = 250000, P/Y = C/Y = 12 gives PMT ≈ $1347.36. $833 is just principal ÷ 300 and $875 is the first month's interest only — both ignore amortization.
A retiree wants to withdraw $800 at the end of every month for 20 years from an account earning 4.8% per annum, compounded monthly. Determine the amount that must be in the account now.
Answer: $123,275
This is the present value of an annuity: TVM with N = 240, I% = 4.8, PMT = 800, FV = 0 gives PV ≈ $123,275. $192,000 is simply 800 × 240, which ignores the interest earned while money remains invested.
A $15,000 loan at a nominal annual rate of 6%, compounded monthly, is repaid with equal monthly payments over 5 years. Which values should be entered in a TVM solver?
Answer: N = 60, I% = 6, P/Y = 12, C/Y = 12
N is the total number of payments (5 × 12 = 60), while I% is always the nominal annual rate (6); the solver divides by P/Y itself. Entering I% = 0.5 would apply the monthly rate as if it were annual.
Lena invests $1200 at the end of every year for 15 years in a fund paying 5% per annum, compounded annually. Calculate the value of the fund immediately after the final deposit, to the nearest dollar.
Answer: $25,894
The future value of this ordinary annuity is 1200 × (1.05¹⁵ − 1)/0.05 ≈ $25,894. $18,000 ignores all interest, and $27,189 would be correct only if deposits were made at the start of each year (annuity due).
A $180,000 loan at 3.6% per annum, compounded monthly, is amortised with equal monthly payments over 20 years. Determine the outstanding balance immediately after the 60th payment, to the nearest hundred dollars.
Answer: $146,300
The monthly payment is about $1053.20; using the TVM solver to find the balance after 60 payments gives ≈ $146,318. $135,000 wrongly assumes the balance falls linearly, but early payments are mostly interest, so the balance falls slowly at first.
A $20,000 car loan at 7.2% per annum, compounded monthly, is repaid with equal monthly payments over 4 years. Calculate the total interest paid over the life of the loan, to the nearest dollar.
Answer: $3078
The monthly payment is ≈ $480.78, so total interest = 48 × 480.78 − 20,000 ≈ $3078. $5760 applies simple interest (20,000 × 0.072 × 4) to the full principal, ignoring that the balance decreases over time.
That was 6 of 36 Amortization and annuities using technology questions.
Practise all 36 freeExplainAO3 · 1–3 marks
Give reasons or causes: say what happens AND why, linking each step with 'because' or 'so that'.
ListAO1 · 1–2 marks
Give the items only, one per line. Extra description earns nothing and costs time.
DistinguishAO3 · 1–3 marks
Make the difference clear for BOTH terms — a definition of one of them is only half an answer.
36 Amortization and annuities using technology questions — free with an account. Spaced repetition, streaks and full exam simulations included.
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