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Annuities are mainly used for retirement purposes, they can be lump-sum payments or a series of payments made at equal intervals.

An annuity is due when payments are made at the beginning of the period. In contrast, the ordinary annuity is where payments are made at the end of the period.

Annuity Due Formula:

FV_{Annuity Due}= PMT x [

]x (1 + i)(1 + i) ^{n}- 1i FV = Future value (final amount)

PMT = Payment per period (cash flow per period)

i = Interest rate

n = Number of paymentsOrdinary Annuity Formula:

FV_{Ordinary Annuity}= PMT x [

](1 + i) ^{n}- 1i If the periodic payment doesn't match the compounding frequency

Annuity Due Formula:

FV_{Annuity Due}= PMT x [

] x (1 + i)[(1 + i) ^{(CY ÷ PY)}]^{n}- 1(1 + i) ^{(CY ÷ PY)}- 1^{(CY ÷ PY)}Ordinary Annuity Formula:

FV_{Ordinary Annuity}= PMT x [

][(1 + i) ^{(CY ÷ PY)}]^{n}- 1(1 + i) ^{(CY ÷ PY)}- 1Where:

CY = Compounds per year (compounding frequency)

PY = Payments per year (payment frequency)

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