what are the amount and present value of an annuity of $100 paable at the beginning of each quarter fro 15 years if the interest rate is 12% compounded quarterly?
Present Value=PMT[(1-(1+i)^-n)/i]
Amount = ?????
To find the present value and amount of an annuity, you can use the following formulas:
Present Value = PMT * [(1 - (1 + i)^(-n)) / i]
Amount = PMT * [(1 + i)^n - 1] / i
First, let's calculate the values needed to substitute into the formulas:
PMT = $100 per year
i = interest rate per compounding period = 12% / 4 = 0.12 / 4 = 0.03 (since interest rate is compounded quarterly)
n = number of compounding periods = 15 years * 4 quarters per year = 60 quarters
Now we can substitute these values into the formulas to find the present value and amount:
Present Value = $100 * [(1 - (1 + 0.03)^(-60)) / 0.03]
Amount = $100 * [(1 + 0.03)^60 - 1] / 0.03
Calculating these values:
Present Value = $100 * [(1 - (1.03)^(-60)) / 0.03]
Amount = $100 * [(1.03)^60 - 1] / 0.03
Present Value ≈ $3,050.338
Amount ≈ $9,992.360
Therefore, the present value of the annuity is approximately $3,050.34 and the future amount is approximately $9,992.36.