Suppose a retiree wants to buy an ordinary annuity that pays her $2,000 per month for 20 years. If the annuity earns interest at 3.5% interest compounded monthly, what is the present value of this annuity?

This is the same old problem. Just using different data.

r = 1 + .035/12 = 1.0029166666

2000 (r^240 - 1)/(r-1)
= 2000 * 1.011702/0.00291666
= $693,738.70

Before posting another of these, try using the formula.

Suppose a retiree wants to buy an ordinary annuity that pays her $2,000 per month for 20 years. If the annuity earns interest at 3.5% interest compounded monthly, what is the present value of this annuity?

To find the present value of the annuity, we need to use the formula for the present value of an ordinary annuity:

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

Where:
PV = Present Value
PMT = Monthly payment
r = Interest rate per compounding period
n = Number of compounding periods

In this case:
PMT = $2,000 per month
r = 3.5% / 12 = 0.00292 (monthly interest rate)
n = 20 years * 12 months/year = 240 months

Substituting the values into the formula:

PV = $2,000 * [(1 - (1 + 0.00292)^(-240)) / 0.00292]

Calculating the inner part of the brackets:

(1 + 0.00292)^(-240) ≈ 0.475

Substituting back into the formula:

PV = $2,000 * [(1 - 0.475) / 0.00292]

Calculating the value inside the brackets:

(1 - 0.475) ≈ 0.524

Substituting back into the formula:

PV = $2,000 * (0.524 / 0.00292)

Calculating the value inside the brackets:

0.524 / 0.00292 ≈ 179.45

Substituting back into the formula:

PV = $2,000 * 179.45

Calculating the product:

PV ≈ $358,900

Therefore, the present value of this annuity is approximately $358,900.

To find the present value of the annuity, you need to calculate the amount of money needed to invest today in order to receive those monthly payments for 20 years. Here's how you can calculate it:

Step 1: Convert the annual interest rate to a monthly interest rate. Since the annuity earns interest at 3.5% compounded monthly, divide the annual interest rate by 12 to get the monthly interest rate: 3.5% / 12 = 0.0029.

Step 2: Calculate the number of months in 20 years. Since there are 12 months in a year, multiply 20 by 12 to get 240 months.

Step 3: Use the present value of an annuity formula to calculate the present value. The formula is:

PV = PMT x [1 - (1+r)^(-n)] / r

Where:
PV = Present Value of the annuity
PMT = Monthly payment
r = Monthly interest rate
n = Number of periods

Substituting the given values:
PMT = $2,000 (monthly payment)
r = 0.0029 (monthly interest rate)
n = 240 (number of months)

PV = $2,000 x [1 - (1+0.0029)^(-240)] / 0.0029

Using a calculator, solve this equation to find the present value of the annuity. The answer is the amount of money the retiree should invest today to receive $2,000 per month for 20 years at a 3.5% interest rate compounded monthly.