If I pay 4 half-yearly installments in an investment scheme or I pay monthly installments of the same time (2 years). Interest rate in both cases is 9% compounded monthly. What will be my future value of annuity? I divided 9% by 12 in order to get the interest rate. For monthly installments, my compounding period is 2*12=24 months but what will be the compounding period (n) if the interest is still monthly compounded? Will there be any difference?
You're missing some key information but I'll take a stab at it since no one else is.
Let's break it into two sections:
===Monthly payments first. ===
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
If you get $2,182.28 or so then don't worry. That's just rounding due to the cash flow (it's actually $83.3333 etc.)
===Semi-Annual payments, but monthly compounding===
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
We need to calculate the effect of compounding during each 6-month period.
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
Now we can calculate the annuity value:
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
The difference between the two annuities is $2,182.37 - $2,141.81 = $40.56 To be candid, that's chump change. What's your real cash flow?
Anyone want to confirm the math is good?