Difference between revisions of "Compound Interest"

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Compound interest includes interest earned on the interest that was previously accumulated.
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'''Compound interest''' includes interest earned on the interest that was previously accumulated.
  
 
Compare, for example, a bond paying 6 percent semiannually (that is, coupons of 3 percent twice a year) with a certificate of deposit (GIC) that pays 6 percent interest once a year. The total interest payment is $6 per $100 par value in both cases, but the holder of the semiannual bond receives half the $6 per year after only 6 months (time preference), and so has the opportunity to reinvest the first $3 coupon payment after the first 6 months, and earn additional interest.
 
Compare, for example, a bond paying 6 percent semiannually (that is, coupons of 3 percent twice a year) with a certificate of deposit (GIC) that pays 6 percent interest once a year. The total interest payment is $6 per $100 par value in both cases, but the holder of the semiannual bond receives half the $6 per year after only 6 months (time preference), and so has the opportunity to reinvest the first $3 coupon payment after the first 6 months, and earn additional interest.
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* [https://mathresearch.utsa.edu/wikiFiles/MAT1053/Simple_and_Compound_Interest/MAT1053_M7.1Simple_and_Compound_Interest.pdf Simple and Compound Interest], Book Chapter
 
* [https://mathresearch.utsa.edu/wikiFiles/MAT1053/Simple_and_Compound_Interest/MAT1053_M7.1Simple_and_Compound_Interest.pdf Simple and Compound Interest], Book Chapter
 
* [https://mathresearch.utsa.edu/wikiFiles/MAT1053/Simple_and_Compound_Interest/MAT1053_M7.1Simple_and_Compound_InterestGN.pdf Guided Notes]
 
* [https://mathresearch.utsa.edu/wikiFiles/MAT1053/Simple_and_Compound_Interest/MAT1053_M7.1Simple_and_Compound_InterestGN.pdf Guided Notes]
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== Licensing ==
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Content obtained and/or adapted from:
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* [https://en.wikipedia.org/wiki/Interest Interest, Wikipedia] under a CC BY-SA license

Latest revision as of 16:03, 24 October 2021

Compound interest includes interest earned on the interest that was previously accumulated.

Compare, for example, a bond paying 6 percent semiannually (that is, coupons of 3 percent twice a year) with a certificate of deposit (GIC) that pays 6 percent interest once a year. The total interest payment is $6 per $100 par value in both cases, but the holder of the semiannual bond receives half the $6 per year after only 6 months (time preference), and so has the opportunity to reinvest the first $3 coupon payment after the first 6 months, and earn additional interest.

For example, suppose an investor buys $10,000 par value of a US dollar bond, which pays coupons twice a year, and that the bond's simple annual coupon rate is 6 percent per year. This means that every 6 months, the issuer pays the holder of the bond a coupon of 3 dollars per 100 dollars par value. At the end of 6 months, the issuer pays the holder:

Assuming the market price of the bond is 100, so it is trading at par value, suppose further that the holder immediately reinvests the coupon by spending it on another $300 par value of the bond. In total, the investor therefore now holds:

and so earns a coupon at the end of the next 6 months of:

Assuming the bond remains priced at par, the investor accumulates at the end of a full 12 months a total value of:

and the investor earned in total:

The formula for the annual equivalent compound interest rate is:

where

r is the simple annual rate of interest
n is the frequency of applying interest

For example, in the case of a 6% simple annual rate, the annual equivalent compound rate is:

Resources

Licensing

Content obtained and/or adapted from: