About Compound Interest, Study notes of Financial Management

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About Compound

Interest

TABLE OF CONTENTS

• About Compound Interest...................................................................................................
  • What is COMPOUND INTEREST?...............................................................................
• Interest.................................................................................................................................
  • Simple Interest
  • Compound Interest..........................................................................................................
• Calculations.........................................................................................................................
  • Calculating How Much to Invest
  • Calculating Rate of Return..............................................................................................
  • Compounding Periodically
• Rules/Contributions
  • Rule of 72 - How to Estimate Compound Interest..........................................................
  • Adding Contributions......................................................................................................
• Annuity
  • Annuities
• Mortgage
  • Mortgages
• Glossary
• References...........................................................................................................................

● Below is a graph that illustrates the difference between simple and

Compound Interest..........................................................................................................

The essential difference is clear: exponential vs. linear growth.

● There are three ways you can calculate compound interest:

• Use a financial calculator, such as the one found at:

http://www.moneychimp.com/calculator/compound_interest_calculato r.htm

• Use a Future Values Table, such as the one found at:

http://members.shaw.ca/RetailInvestor/futurevaluetables.pdf

• Use a formula.

● Let us begin to use some calculations to find compound interest:

To derive the formula, let us go through the calculations again using symbols instead of numbers. Let P be the amount of principal invested (or borrowed). Let r be the annual interest rate, and let n be the number of years.

Then, you get:

After year 1: P + Pr = P(1 + r) After year 2: [P(1 + r)] + r[P(1 + r)] = P(1 + r)(1 + r) After year 3: [P(1 + r)(1 + r)] + r[P(1 + r)(1 + r)] = P(1 + r)(1 + r)(1 + r)

After n years: P(1 + r)n

This gives us a formula we can use when money is compounded annually.

Future Value (FV) = P(1 + r)n

Calculations

Calculating How Much to Invest

● Sometimes, instead of wanting to know the future value of your investment, you want to know how much you will need to invest to generate the amount of money you require: this is called "present value."

● If we take the equation FV = P(1+r)n, solving for P, we get P = FV/(1+r)n. It is traditional to change the P to PV to stand for "present value," instead of "principal." So, the formula to use is:

Present Value = PV = FV / (1 + r)n

Calculating Rate of Return..............................................................................................

● You can also solve the equation FV = PV (1+r)n^ for the interest rate: This is called the "rate of return," the interest rate you need to get the amount of money you require.

● Solving for r, the formula is:

Rules/Contributions

Rule of 72 - How to Estimate Compound Interest..........................................................

● Imagine you are discussing making an investment, at a restaurant, with no calculator or computer handy. You can use the Rule of 72 to figure out how long it will take to double your money.

The number of years required is approximately 72/r, where r is the interest rate expressed as a percentage, and the investment is compounded annually.

● If you know the number of years, n, you can calculate the interest rate you need to double your money using the formula 72/n. This estimate works well, as long as the interest rate is not too high.

Adding Contributions......................................................................................................

● People making an investment often want to make contributions to it as it grows.

● Generally, for P = principal, r = interest rate, c=annual contribution, and n=number of years, we have:

Annuity

Annuities

● Sometimes, instead of putting money into an investment, you want to take money out: this is called an annuity.

● Here is the general form for finding annuity:

where P=principal, r=rate, and n=number of years.

Mortgage

Mortgages

● Mortgages work somewhat like annuities, except that you make payments, as opposed to receiving them.

● Working with symbols, instead of numbers, the formula is:

● Each time you make a payment on a mortgage, part of the payment is interest and part of the payment is equity. It is important to know which is which.

● The equity is the amount of money you would be able to keep if you sold the house; the interest might be tax deductible. The easiest way to calculate this is using a spreadsheet. Make three columns: balance, interest, and equity. The balance is last year's balance plus last year's interest. The interest is the balance times the interest rate. The equity is the annual payment minus the interest.

Real Interest Rate: a subtraction of the inflation rate from the

effective interest rate.

Simple Interest: interest calculated based on the principal

alone.

References

http://en.wikipedia.org/wiki/Compound interest