Compound interest is the interest either loan or deposit, calculated on the initial deposit (principal) and the accumulated interest from the previous period.
Total interest = FV - P
Where:
FV = Future value
P = Initial principal balance
Formula:
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FV = Future value (final amount)
P = The initial investment (initial principal balance)
r = Interest rate
n = Number of times compounded per year
t = Term (number of time periods)
Formulas if there are contributions:
If the additional deposit is made at the end of the period, it can be the end of the month, quarter, year, etc...
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FV = [P x (1 + r ÷ n )(n x t)] + [ PMT x [((1 + r ÷ n)(n x t) - 1) ÷ (r ÷ n)] ]
If the additional deposit made at the beginning of period
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FV = [P x (1 + r ÷ n )(n x t)] + [[ PMT x [((1 + r ÷ n)(n x t) - 1) ÷ (r ÷ n)] ] x ( 1 + r ÷ n )]
Where PMT is the additional payment
If the periodic payment doesn't match the frequency of compounding.
Formula will be:
FV = [P x (1 + r ÷ n )(n x t)] + [ PMT x ([(1 + r ÷ n)(n x NP)](NP x t) -1) ÷ [(1 + r ÷ n)(n x NP) -1] ]
Where NP is the number of payment per year