What is the present value of an ordinary annuity which has payments of $1100 per year for 19 years at 5% compounded annually.
To calculate the present value of an ordinary annuity, you 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 payment per year (PMT) is $1100, the interest rate (r) is 5%, and the number of years (n) is 19.
To find the present value, follow these steps:
Step 1: Convert the annual interest rate to the interest rate per compounding period.
Since the interest is compounded annually, the interest rate per period (r) is simply the annual interest rate divided by the number of compounding periods in a year. Here, the interest rate per period would be 5% / 1 = 5%.
Step 2: Plug the values into the formula and calculate.
Using the formula mentioned earlier, plug in the values:
PV = $1100 * [(1 - (1 + 0.05)^(-19)) / 0.05].
Step 3: Solve the equation.
Now, solve the equation using a calculator or spreadsheet. The present value (PV) should be calculated as:
PV = $1100 * [(1 - 1.05^(-19)) / 0.05].
= $1100 * [(1 - 0.376889) / 0.05].
= $1100 * [0.623111 / 0.05].
= $1100 * 12.46222.
≈ $13,708.44 (rounded to two decimal places).
Therefore, the present value of the ordinary annuity with payments of $1100 per year for 19 years at 5% compounded annually is approximately $13,708.44.