Question

What is the present value of an ordinary annuity that pays $37,000 at the end of each of the next 18 years if the discount rate is 11% ? Answer Format: Enter your answer as a number rounded to 2 decimal places. An answer of 23.456 would be entered as 23.46.

Answer 1

The present value of an ordinary annuity that pays $37,000 annually for 18 years at a discount rate of 11% is $30,308.67.

Step-by-step explanation:

The present value of an ordinary annuity that pays $37,000 at the end of each of the next 18 years with a discount rate of 11% can be calculated using the present value formula for annuities. The formula is:

PV = Pmt * [1 - (1 + r)^(-n)] / r

Where:

• PV = present value of the annuity
• Pmt = annual payment ($37,000)
• r = discount rate (11% or 0.11)
• n = number of periods (18 years)

Using this formula:

PV = $37,000 * [1 - (1 + 0.11)^(-18)] / 0.11

PV = $37,000 * [1 - (1 + 0.11)^(-18)] / 0.11

PV = $37,000 * [1 - 1/((1 + 0.11)^18)] / 0.11

PV = $37,000 * [1 - 1/(5.537476)] / 0.11

PV = $37,000 * [1 - 0.180579] / 0.11

PV = $37,000 * 0.819421 / 0.11

PV = $30,308.67

Therefore, the present value of the annuity is $30,308.67 when rounded to two decimal places.