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grade12_financial_maths_quiz2 draws its questions at random from a bank of 24 questions, with full worked solutions for every one.
A few of the question types, with full solutions, so you know what to expect.
An account pays \(12\%\) p.a. compounded monthly. State \(i\) and \(n\) for 3 years.
Answer: \(i=0{,}01\) and \(n=36\)
\(i=\dfrac{0{,}12}{12}=0{,}01\text{ per month}\)
\(n=3\times 12=36\text{ months}\)
*\(\text{The units of } i \text{ and } n \text{ must always match.}\)
Which process is linear?
Answer: Simple interest
\(\text{Simple interest adds the same rand amount each period: } A=P(1+in).\)
\(\text{The other three are exponential.}\)
R10 000 is invested for 3 years at \(8\%\) p.a. simple interest. Find the accumulated value.
Answer: R12 400,00
\(A=P(1+in)\)
\(=10\,000(1+0{,}08\times 3)\)
R10 000 is invested for 3 years at \(8\%\) p.a. compounded annually. Find the accumulated value.
Answer: R12 597,12
\(A=P(1+i)^{n}=10\,000(1{,}08)^{3}\)
*\(\text{Higher than simple interest because interest earns interest.}\)
A vehicle costing R320 000 depreciates at \(16\%\) p.a. on the reducing balance. Find its value after 3 years.
Answer: R189 665,28
\(A=P(1-i)^{n}=320\,000(0{,}84)^{3}\)
*\(\text{Reducing balance uses } (1-i)^{n}\text{, not } (1-in).\)