suppose the interest rate is 8% apr with monthly compounding. what is the present value of an annuity that pays $95.00 every 6 months for 6 years.
You can earn an expected return of 13 percent compounded semiannually. If you invest $400 today, then you would have $ in 22 years
To calculate the present value of an annuity, we can use the formula:
PV = PMT * [1 - (1 + r)^(-n)] / r
Where:
PV = Present Value
PMT = Payment per period
r = Interest rate per period
n = Number of periods
In this case, the interest rate is 8% APR (Annual Percentage Rate) with monthly compounding. To convert it to the interest rate per period, we need to divide it by the number of compounding periods in a year. Since the compounding is monthly, there are 12 periods in a year.
r = 8% / 12 = 0.08 / 12 = 0.0066667 (rounded to 7 decimal places)
The annuity pays $95.00 every 6 months for 6 years. Since compounding is monthly, there are 2 periods in a year (6 months / 12 months per year = 0.5).
n = 6 years * 2 periods/year = 12 periods
Now we can plug these values into the formula:
PV = $95.00 * [1 - (1 + 0.0066667)^(-12)] / 0.0066667
Using a calculator, we can evaluate the expression inside the brackets:
[1 - (1 + 0.0066667)^(-12)] / 0.0066667 ≈ 6.2383
Finally, we multiply the result by the payment per period:
PV ≈ $95.00 * 6.2383 ≈ $592.71
Therefore, the present value of the annuity that pays $95.00 every 6 months for 6 years, with an interest rate of 8% APR and monthly compounding, is approximately $592.71.