Lauretta J. Fox
Simple interest is computed on a principal which remains unchanged for a specific period of time. Compound interest is calculated on a principal that changes at the end of stated time period when interest is added to it. The time period may be any interval during the year such as annually, semiannually, quarterly, monthly or daily. When simple interest is added to the principal it is said to be compounded, that is, the sum becomes the new principal to be used during the next interest period. The difference between the original principal and the amount it has become at the end of any period of time is known as compound interest.
To calculate compound interest, divide the annual rate of interest by the number of interest periods in the year. Multiply the result by the principal to obtain the interest for the period. Add this amount to the principal to find the new principal at the beginning of the next
interest period. Repeat this procedure for the desired number of interest periods. The difference between the final amount and the original principal is the compound interest accumulated.
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Example:
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John invested $500 at 6% compounded monthly. How much compound interest did he earn during the tour months?
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Solution:
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Monthly rate of interest is 6% 12 .5%
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Balance at
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Balance at
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Beginning
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End of
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Month
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of Month
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Interest
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Month
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1
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$500.00
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.5/100500/12.50
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$502.50
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2
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$502.50
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.5/100 x 502.50/1
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= 2.51
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$505.01
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3
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$505.01
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.5/100 x 505.01/1
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= 2.53
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$507.54
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4
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$507.54
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.5/100 x 507.54/1
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= 2.54
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$510.08
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$510.08 $500.00 = $10.08 Compound Interest Earned in 4 most
Solve the following set of problems.
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1. How many interest periods are there in six years if interest is compounded and paid annually? Quarterly? Semiannually? If the interest rate is 10% per year, what is the interest rate per period of time for each of these interest periods?
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2. If a person deposits $500 in a savings account, how much will he have at the end of two years if the interest is compounded semiannually at 5.5% per year? ‘What amount of compound interest will he earn?
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3. Mary invested $2,500 at 8% interest per year compounded quarterly. How much did she have at end of 1 1/2 years? How much compound interest did she receive?
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4. How much more compound interest will $850 earn at 6.5% compounded quarterly as compared to semiannually at the rate of 14% per year?
