Understanding Compound Interest

14 Jun

As always, this lesson is not intended to be professional advice. This is simply lesson material for ESL students in a Managerial Economics and Corporate Finance class. Posted here for their use or for helping other students.

Corporate Value (值)

Financial officers and Managers are extremely responsible for the monetary (货币) goings-on in their companies. As we said before, the Wealth Maximization Rule means that Financial and Corporate Managers are required to maximize (最大化) the profits (收益) for their investors (投资者). 

However, maximizing profits requires in-depth (深入)planning and micro-managing (微观) your funds today while considering (考虑) future profits as well.

There are two types of Value (值) that you should be aware of in Finance and Economics.

The first is called Present Value (现值) and is the value today of something that will increase in value in the future. ExampleWhen we loan someone $1,000 at 10% interest, we know that our $1,000 loan will increase in value in the future. Present Value = PV.

The second is called Future Value (未来价值) and is the value that the item will have in the future. Future Value = FV.

Interest (利)

I’ll make another post later discussing the many ways to use Present and Future value in your company, but today I just wanted to talk about using them to calculate (计算) “Compound Interest” (复利).  

Usually, when we loan money to someone or invest (投资) our money in something, we do so on the condition that we receive back more money than we put in.  Our corporation is not a charity (慈善机构), we don’t loan you things for free!  The original money we invest is called the Principal (本息).  The extra money we get on top is called the Interest (利).  

Example ~ Company A (a large global corporation) invests $100,000 in a small new business called Company B.  Company B has 10 years to pay it back. But Company A doesn’t do this for free ~ they want to maximize their profits too. That means they have to make some money on this contract (合同).  So they ask Company B to pay an additional 7% per year.   

$100,000 = Principal
7% = Interest

COMPOUND INTEREST (复利)

Problem! ~ 7% of what?  
Answer! ~ It depends:)   It depends on how Company A decides to count it.

There are two separate mathematical formulas (数学公式) you can use to figure out the Interest.  

The first one is called Simple Interest (单利) and I’ve already looked at it before.

The second method is called Compound Interest (复利). Compound Interest says that each payment period, Company B is going to pay an additional 7% of the currently owed principal! Lenders and Investors really like compound interest a lot better than simple interest.  

For example: I borrow $1000 due in two years.  My interest rate is 10%.  

If I use Simple Interest:  Year 1, I owe $1000 + 10% interest = $1100.  Year 2, I owe $1100 + (10% of $1000) = $1200. :) 

If I use Compound Interest: Year 1, I owe $1000 + 10% interest = $1100.  Year 2, I owe $1100 + (10% of $1100) = $1210

The formula for Compound Interest is:

I = Interest
P = Present Value
R = Interest Rate
T = Number of Years Involved
N = Number of Times a Year

Example 

Company A (a large global corporation) invests $100,000 in a small new business called Company B.  Company B has 10 years to pay it back. The interest rate is 7% compounded  bi-annually.   What is the Total Interest (利) you will pay over 10 Years?

Calculating FUTURE VALUE and PRESENT VALUE using COMPOUND INTEREST

The total interest is of course important to both Company A and Company B, there are two other important numbers that the financial managers of Company A want to know–the Present Value of their money and the Future Value of their money.  

Future Value

FV = Future Value (how much money you will make in total)
PV = Present Value

R = Interest Rate
T = Number of years involved
N = Times per Year

Using our example above with Company A & B, the Future Value is calculated like this:

That means Company A will make a total of $286,968.46 if they invest their $100,000 in Company B now. Over 10 years, their $100,000 will change into $386,968.46.:) We like this plan!

Present Value

Sometimes, for example with bonds (债券), we know the Future Value (how much money will be paid to us in the end). But we don’t know how much money has to be invested (Present Value) to get that future result.  So Present Value is calculated by the formula: 

PV = Present Value 
FV = Future Value

R = Interest Rate
T = Number of years involved
N = Number of Times per Year

Example: Mary Jane knows that in 4 years, she needs to have a total of $150,000 to pay her college tuition. She has an interest-generating account that gives her a 4% compound interest rate bi-annually on everything she puts in. How much money should she invest today (Present Value) in order to have $150,000 in 4 years?

That means that Mary Jane needs to put $101,336.67 in her bank account now in order to get $150,000 in the future. 

JPEG

KEY TERMS TO REMEMBER

  1. Value (值)
  2. Present Value (现值)
  3. Future Value (未来价值)
  4. Interest (利)
  5. Simple Interest (单利)
  6. Compound Interest (复利)
  7. Principal (本息)
  8. Monthly (每月一次)
  9. Weekly (每周)
  10. Annually (每年)
  11. Bi-Annually (一年两次)
  12. Quarterly (季刊)

FORMULAS TO REMEMBER

Compound Interest

Future Value

Present Value

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