Te falta información clave, pero voy a intentarlo ya que nadie más lo hace.
Vamos a dividirlo en dos secciones:
\===Los pagos mensuales primero. ===
Cash flow: $1,000 per year, with first monthly payment due in 30 days.
Term: 2 years, with final value computed at end of 24th month,
including the final payment due at that time.
Annual rate: 9.00%
Compounding: 12 periods per year (monthly)
Cash flow = $1,000 / 12 = $83.33 per month; first payment due in 30 days.
Rate = 0.09 / 12 = 0.0075 per month (in decimal)
Num period = 12/yr x 2yrs = 24
FVA = $2,182.37 [= $83.33 x ((((1 + 0.0075)^24)-1)/0.0075)]
Annuity = $1,000 x 2yrs = $2,000
Value = $2,182.37 - $2,000 = $182.37
Si consigues $2,182.28 or so then don't worry. That's just rounding due to the cash flow (it's actually $ 83,3333 etc.)
\===Pagos semestrales, pero compuestos mensualmente===
Cash flow: $1,000 per year, with first payment due in 183 days.
Term: 2 years, with final value computed at end of 24th month,
including the final payment due at that time.
Annual rate: 9.00%
Compounding: 12
Tenemos que calcular el efecto de la capitalización durante cada período de 6 meses.
Rate = 0.09 / 12 = 0.0075 per month (in decimal)
Num period = 12/yr / (2/yr) = 6
Rate = (1 + 0.09/12)^6 - 1
= 0.04585 semi-annual
Num period = 1
Ahora podemos calcular el valor de la anualidad:
Cash flow = $1,000 / 2 = $500 semi-annual, with first payment due in 183 days.
Rate = 0.04585 (in decimal)
Num period = 2/yr x 2yrs = 4
FVA = $2,141.81 ($500 x ((((1 + 0.04585)^4)-1)/0.04585)]
Annuity = $1,000 x 2yrs = $2,000
Value = $2,141.81 - $2,000 = $141.81
La diferencia entre las dos anualidades es $2,182.37 - $ 2,141.81 = $40.56 Para ser sincero, eso es calderilla. ¿Cuál es tu flujo de caja real?
¿Alguien quiere confirmar que las matemáticas son buenas?
