Definition:Interest/Compound
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Definition
Compound interest is interest which is calculated by:
at the end of agreed conversion periods.
Such interest is said to be compounded according to that conversion period.
Examples
Arbitrary Example
Let $\pounds 1000$ be invested for $2$ years at $8 \%$ per annum.
Let interest be compounded half-yearly.
At the end of the $1$st $6$ months, the compound interest will be:
- $I_1 = \dfrac 8 {100} \times \dfrac 1 2 \times \pounds 1000 = \pounds 40$
At the end of the $2$nd $6$ months, the compound interest will be:
- $I_2 = \dfrac 8 {100} \times \dfrac 1 2 \times \pounds 1040 = \pounds 41 \cdotp 60$
At the end of the $3$rd $6$ months, the compound interest will be:
- $I_3 = \dfrac 8 {100} \times \dfrac 1 2 \times \pounds 1081 \cdotp 60 = \pounds 43 \cdotp 26$
At the end of the $4$th $6$ months, the compound interest will be:
- $I_4 = \dfrac 8 {100} \times \dfrac 1 2 \times \pounds 1124 \cdotp 86 = \pounds 44 \cdotp 99$
Hence the total interest earned will be $\pounds 169 \cdotp 85$.
Also see
- Results about compound interest can be found here.
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): compound interest
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): interest
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): compound interest
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): interest