suppose the interest rate is 8% APR with monthly compounding. What is the present value of an annuity that pays $90 every 6 months for 5 years?
12
To calculate the present value of an annuity, you need to use the formula:
PV = C * [1 - (1 + r)^(-n)] / r
Where:
PV = Present value (or the desired value in today's dollars)
C = Cash flow per period (in this case, $90)
r = Interest rate per period (8% APR, compounded monthly, so divide by 12 for monthly interest rate: 8% / 12 = 0.67% or 0.0067)
n = Total number of periods (5 years, with payments every 6 months, so total periods will be 2 * 5 = 10)
Now, let's substitute the values into the formula and calculate:
PV = $90 * [1 - (1 + 0.0067)^(-10)] / 0.0067
Using a calculator, the calculation will be as follows:
PV = $90 * [1 - (1 + 0.0067)^(-10)] / 0.0067
≈ $90 * (1 - 0.880348789) / 0.0067
≈ $90 * 0.119651211 / 0.0067
≈ $1078.79991
Therefore, the present value of the annuity that pays $90 every 6 months for 5 years, given an 8% APR with monthly compounding, is approximately $1078.80.