Compound Interest Introduction Calculating Compound Interest

Module 4 ? Calculations Related to Source Documents Class 8-9: Compound Interest

Compound Interest Introduction

We know that simple interest is calculated only once for the duration of a loan or investment. For example, if you invested $1000 for three years, the bank will figure the interest at the end of the three years and then give you the interest. Compound interest is calculated more often, and as soon as it is calculated, it is added to the original principal and also starts to earn interest. In other words, when interest is calculated using the compound interest method, you earn interest on interest. This is why it is good to receive compound interest, but not to pay it.

Calculating Compound Interest

If you borrowed $5,000.00 at an interest rate of 7% compounded annually for 4 years, how much interest would you pay at the end of the four years? Compounded annually simply means that the interest is only calculated once a year.

We can calculate the interest by using the multi-step method of calculating compound interest. When doing the calculations using this method, it is very similar to calculating simple interest.

This method is shown on the following page:

Multi-Step Method of Calculating Compound Interest

Step 1 Find the principal for the 1st year

Amount borrowed = $5,000.00

Step 2 Find the interest for the 1st year $5,000.00 * 7%

+ $350.00

Step 3 Find the principal for the 2nd year $5,000.00 + 350.00

= $5,350.00

Step 4 Find the interest for the 2nd year $5,350.00 * 7%

+ $374.50

Step 5 Find the principal for the 3rd year $5,350.00 + 374.50

= $5,724.50

Step 6 Find the interest for the 3rd year $5,724.50 * 7%

+ $400.715

Step 7 Find the principal for the 4th year $5,724.50 - $400.715

= $6125.215

Step 8 Find the interest for the 4th year $6,125.22 * 7%

Step 9 Find the total amount owing

$6,125.215 + $428.76505

+ $428.76505 = $6,553.98

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Module 4 ? Calculations Related to Source Documents Class 8-9: Compound Interest

At the end of four years, you would owe $6,553.98. Since the original principal was $5,000.00, you would pay $1,553.98 interest.

Notice that when computing the interest for each year, the answers were not rounded. Since interest earns interest, rounding could reduce the amount of interest earned each year. Only the final answer should be rounded to the nearest cent.

Exercise

Using the multi-step method, calculate the total amount to be paid on a loan of $3,000 at a rate of 9% for four years.

Instructions

The answer must be rounded up to 2-decimal.

Step 1 Step 2 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 Step 9

Find the principal for the 1st year Find the interest for the 1st year Find the principal for the 2nd year Find the interest for the 2nd year Find the principal for the 3rd year Find the interest for the 3rd year Find the principal for the 4th year Find the interest for the 4th year Find the total amount owing

= $3,000 + $270.00 = $3,270 + $294.30 = $3,564.30 + $320.79 = $3,885.09 + $349.66 = $4,234.75

The total amount to be paid on the loan is $4,234.75.

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Module 4 ? Calculations Related to Source Documents Class 8-9: Compound Interest

Compounding Periods

In the examples on the previous page, the compound interest was paid at the end of each year, or annually. In fact, compound interest is usually paid more than once a year. The amount of time between the calculations of interest is called the compounding or conversion period. This simply means how many times in one year the interest is calculated. Some common compounding periods and the number of times the interest is calculated for each period are shown below:

? Annually - interest is paid once a year. ? Semi-annually - interest is paid twice a year (every 6 months) ? Quarterly - interest is paid 4 times a year (every three months) ? Monthly - interest is paid 12 times a year (every month) ? Daily - interest is paid 365 times a year (every day)

Remember, interest is stated for a year, so you must find the interest rate per period before calculating compound interest. To find the rate for a given period, divide the rate by the number of periods. For example, if the interest rate is 8%, compounded quarterly, (4 times a year), the interest rate for each period is

8%/4 = 2% per period

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Module 4 ? Calculations Related to Source Documents Class 8-9: Compound Interest

Exercise

Find the interest rate per period for the following rates and periods. Use only as many places after the decimal as necessary, with a maximum of 2.

Instructions:

Calculate the percentage of Interest Rate per Period.

Compounding Period

Annually

Rate 10%

Interest Rate

per Period

10%

Quarterly 12%

3%

Daily

15% 0.04%

Semi annually 18%

9%

Monthly

24%

2%

Quarterly

8%

2%

Monthly

9% 0.75%

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Module 4 ? Calculations Related to Source Documents Class 8-9: Compound Interest

Problem

Using the multi-step method, calculate how much interest you would earn on an investment of $2000.00 at 12% interest rate compounded quarterly for 1 year. Round all dollar values to 2 decimal places.

Solution

Step 1 Find the interest rate per period Step 2 Find the principal for the 1st quarter

= 12%/4 = 3%

=

$2,000.00

Step 3 Find the interest for the 1st quarter

+

$60.00

Step 4 Find the principal for the 2nd quarter

=

$2,060.00

Step 5 Find the interest for the 2nd quarter

+

$61.80.00

Step 6 Find the principal for the 3rd quarter

=

$2,121.80

Step 7 Find the interest for the 3rd quarter

+

$63.65

Step 8 Find the principal for the 4th quarter

=

$2,185.45

Step 9 Find the interest for the 4th quarter

Step 10

Find the total amount earned.

+

$65.56

=

$2,251.01

The total interest earned on the investment is $251.01

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