IB Mathematics SL 1.7 Amortization and annuities using technology AI HL Paper 1- Exam Style Questions- New Syllabus
Question
| Loan Option | Loan Size (% of purchase price) | Nominal Annual Interest Rate (compounded monthly) |
|---|---|---|
| A | 100% (no initial payment required) | 7.15% |
| B | 80% (requires a 20% initial payment from Raul) | 6.40% |
(ii) Option B.
(ii) Option B.
Most-appropriate topic codes (IB Mathematics: Applications and Interpretation HL):
• SL 1.4: Financial applications of geometric sequences and series — part (a)
▶️ Answer/Explanation
(a)
(i) Option A:
Loan amount \( PV = 42 695 \) USD.
Term \( N = 6 \times 12 = 72 \) months.
Monthly interest rate \( i = \frac{7.15\%}{12} \approx 0.0059583 \).
Using the amortisation formula (or GDC finance app):
Monthly payment \( PMT \approx 730.99 \) USD.
\( \boxed{730.99 \, \text{USD}} \)
(ii) Option B:
Initial payment = \( 20\% \times 42 695 = 8539 \) USD.
Loan amount \( PV = 42 695 – 8539 = 34 156 \) USD.
Monthly interest rate \( i = \frac{6.40\%}{12} \approx 0.0053333 \).
Using the same formula:
Monthly payment \( PMT \approx 572.54 \) USD.
\( \boxed{572.54 \, \text{USD}} \)
(b)
(i) Reason for Option A:
Raul might choose Option A because he does not have sufficient savings for the 20% initial payment, or prefers to keep his cash for other expenses.
“He may not have the funds available for the upfront payment.”
(ii) Reason for Option B:
Option B offers lower monthly payments and, because of the lower interest rate, will likely result in less total interest paid over the life of the loan.
“It requires lower monthly repayments and reduces the total interest paid.”