Find the present value of the ordinary annuity.

Question

Find the present value of the ordinary annuity. (Round your answer to the nearest cent.)

$150/month for 13 years at 3%/year compounded monthly

Thanks!

Answer 1

According to investopedia, "An ordinary annuity is a series of equal payments made at the end of consecutive periods over a fixed length of time."

Three variables are present when calculating the present value of the ordinary annuity:

r, the interest rate per period

PMT, the period of the cash payment

n, the total number of periods

The equation to calculate the present value is:

Present Value = PMT * ( (1 - (1 + r) ^{- n} ) / r )

In this problem, PMT = $150/month, r = 3%/year compounded monthly, and n = 13 years.

The compounding is monthly, so we will convert the years to months:

PMT = $150/month

r = 3%/year = 3% / 1 year * 1 year / 12 months = 0.25% / month = 0.0025 / month

n = 13 years = 13 years * 12 months / 1 year = 156 months

Present Value = 150 * ( ( 1 - (1 + 0.0025)^-156 ) / 0.0025 ) = 150 * ( ( 1 - 0.67738647084) / 0.0025) = 150 * 129.045411664 = $19,356.82