Here is a table of the first six months of balances and interest payments. In fact, spreadsheets are very good at this kind of work. The reason is that each balance calculation is found by a simple formula from the previous. I_n = A_Īlthough it seems complicated at first, the formula for A_n, which is called a recursive definition for the sequence, helps us to compute all of the balances very quickly. First, the interest payment is always equal to the previous balance times 0.005. Altogether then, the new balance will be:Ī_2 = 9750 - 251.25 = 9498.75īut now in order to automate the process, let’s write everything in terms of I_n and A_n. That would leave 300-48.75=251.25 for paying off the loan. To compute the balance after the second month, we repeat the same steps. By convention, we write A_0 = 10,\!000 for the initial amount of the loan (let’s not worry about the dollar signs going forward). Therefore out of the first $300, only $250 will go towards paying off the loan. et I_n stand for the interest payment in month n. Each month, the bank charges 0.5% interest (6\% \div 12), or as a decimal: 0.005. What do I need to know about applications of arithmetic sequences and series If a sequence seems to fit the pattern of an arithmetic sequence it can be said. First of all, the bank will tack on interest. In fact, you might already believe that 0. Let’s work out the first month carefully. 12 sequences and series This is less ridiculous than it appears at rst. Therefore, it is incorrect to say 'the sum of this sequence is 10' when what you really mean is 'the sum of this series is 10. This is part of the HSC Mathematics Advanced course under the topic of Financial Mathematics: Arithmetic sequences and series. A sequence is a list of numbers that follow a pattern or rule, while a series is the sum of the terms in a sequence. That is, we will examine the sequence of balances. Sequence and series are two different mathematical concepts that should not be used interchangeably. However we can still answer the questions by finding out exactly what is still left to pay after each month. To answer these questions quickly, we would have to know about certain loan formulas. How long will it take to pay off the loan? How much interest will you end up paying? Suppose that the monthly payments were fixed at $300 by the lender. When the loan is in repayment, it will accrue 6% annual interest, compounded each month. So any time you have data arranged in a list, you may require methods from sequences and series to analyze the data.įor example, suppose you take out a small student loan for $10,000. Learn more about our Matrix+ Online Maths Adv Course now.A sequence is simply a list of numbers, and a series is the sum of a list of numbers. Learn from expert Maths teachers at the comfort of your own home! You will have access to theory video lessons, receive our comprehensive workbooks sent to your front door, and get help through Q&A discussion forums with Matrix+ Online Courses.
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