新SAT数学知识点介绍④：Simple Interest & Compound Interest By JianYu

今天我们一起来继续聊一聊SAT数学知识点 —— Simple Interest & Compound Interest，事实上我们大部分同学在初高中阶段都应该已经接触这两个知识点，但事实上在我的教学生涯和往期TD学员中，还是会遇到不少同学在这个知识点上会出现一些理解偏差。那在SAT数学里，它们的考点和考试形式又是什么样的呢？

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① 知识点介绍

Simple interest 是指按照固定的本金计算的利息，是计算利息的一种方法。单利的计算取决于本金，单利的增长曲线是线性增长。

Compound interest 就是传说中的「利滚利」，每经过一个计息期后，都要将所生利息加入本金，以计算下期的利息。复利的增长曲线是指数增长。

① 计算公式

计算公式是解决这类题目最为重要的依仗手段，基本上做这一类题目都需要熟练地应用对应计算公式。

Know the formulas for simple and compound interest.

**Simple interest：A = P(1 + rt) **
**Compound interest：A = P(1 + r/n)^nt **

A is the total amount, P is the principal, r is the interest rate expressed as a decimal, t is the time period, and n is the number of times the interest is compounded per year.

同学们在解决这类题目的时候，首先要判断题中所求的interest的种类是哪一种「Simple or Compound」，如果是Compound Interest，一定要看清这个interest一年会compound几次（也就是公式中的n值）「这是易错点」。

③ OG例题讲解

A bank has opened a new branch and, as part of a promotion, the bank branch is offering $1,000 certificates of deposit at an interest rate of 4% per year, compounded semiannually. The bank is selling certificates with terms of 1, 2, 3, or 4 years. Which of the following functions gives the total amount, A, in dollars, a customer will receive when a certificate with a term of k years is finally paid?

A) A = 1,000(1 + 0.04k)
B) A = 1,000(1 + 0.08k)
C) A = 1,000(1.04)^k
D) A = 1,000(1.02)^2k

解析

做这类题目的思路首先点判断利息的种类，通过题目我们可以得知这是Compound Interest；接下来我们要判断一年Compound的次数，题中告知我们「deposit at an interest rate of 4% per year, compounded semiannually」即每半年结算一次，也就是说一年两次，结合TD学员的往期表现来看，这个地方是最易出错的点。

所以我们套用公式 A = P(1 + r/n)^nt ，P=1000，r=0.04，n=2。即可得到正确选项D。

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OG样题练习

A bank has opened a new branch and, as part of a promotion, the bank branch is offering $1,000 certificates of deposit at simple interest of 4% per year. The bank is selling certificates with terms of 1, 2, 3, or 4 years. Which of the following functions gives the total amount, A, in dollars, a customer will receive when a certificate with a term of k years is finally paid?

A) A = 1,000(1.04k)
B) A = 1,000(1 + 0.04k)
C) A = 1,000(1.04)^k
D) A = 1,000(1 + 0.04^k)

解析

这道题目考的还是比较常规的，还是老套路，我们首先判断利息的种类。题中已经提到了这是 simple interest。那接下来就很好办了，直接套用公式 A = P(1 + rt)，即可得出正确答案B。

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总结

这一块知识点的主要核心就是「理解并应用对应公式」，大部份题目只要套用公式即可做出来，对考生们来说，所需要注意的 —— 就是正确的使用公式，且需要套公式时不要搞错对应参数即可。

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