Zadanie 8d, Paper 2, listopad 2023, TZ1, Matematyka AA IB SL
Wzorowane na: Matematyka AA IB SL — listopad 2023, TZ1, Paper 2 (zadania wzorowane), pytanie 8(d). Treść, dane i kontekst są zmienione; sprawdzane umiejętności, format i punktacja jak w oryginale.
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Zadanie
Wspólne informacje do wiązki zadań
A research project can choose a grant schedule with payments at the start of each month for 24 months. Plan A pays 3000 dollars each month. Plan B starts at 1800 dollars, with each later payment 5% larger than the previous one. Grant receipts are retained without interest. Separately, a90000-dollar reserve is deposited on the day of the first grant payment and earns nominal annual interest 4.8%, compounded monthly at each month-end; there are no withdrawals or additional reserve deposits. For parts 8c use Plan B. In parts 8a(ii),8c(i),8d give two decimal places.
Polecenie
After the grant ends,25000 dollars are invested for five years at a nominal annual rate r%, compounded quarterly. The balance becomes 34000 dollars. Find r.
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Odpowiedź z klucza
25000(1 + r/400)20 = 34000. Hence r = 400[(34000/25000)1/20 − 1] = 6.197210614…, so r=6.20%.
Schemat punktowania
M1:use compound interest or a financial solver. A1:correct equation or full inputs:20 periods, no payments, present value 25000 and future value 34000 with opposite cash-flow signs, quarterly compounding. A1:6.20%, with the one-time shared precision rule. Financial-solver alternative inputs are N=5 years, P/Y=1, C/Y=4, PMT=0 and opposite signs for PV=25000/FV=34000; equivalently N=20, P/Y=C/Y=4. Award M1 for an attempted financial-solver calculation with at least two entries shown, even when some other entries are incorrect.
Komentarz. Paper 2: calculator and AA SL formula booklet allowed. Retain intermediate precision. Use three significant figures unless exact answers or two decimal places are requested.