Bond Valuation: Pricing an Ordinary Annuity

Finding the Present Value of an Ordinary Annuity

In the realm of finance, annuities serve as crucial financial tools for retirement planning, loan payments, and investment evaluation. The present value of an ordinary annuity refers to the current worth of a stream of regular cash flows received or paid at equal intervals over a specified period. Understanding the concept of the present value of an ordinary annuity is vital for assessing the current value of future cash flows and making informed financial decisions.

Formula for Present Value of an Ordinary Annuity

The present value (PV) of an ordinary annuity can be calculated using the following formula:

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

Where:

PV = Present value of the annuity

P = Periodic payment amount

r = Interest rate per period

n = Number of periods

Example: Phone Carrier Payment Plan

Let's consider a scenario where you plan to finance the purchase of a phone by taking out a loan. The loan terms include monthly payments of $50 for a period of 24 months, with an interest rate of 5% per year. By calculating the present value of this ordinary annuity, you can determine the initial amount required to finance the purchase:

P = $50 (monthly payment)

r = 0.05 (interest rate per month)

n = 24 (number of months)

The present value (PV) can be found using:

PV = (50 * [1 - (1 + 0.05)^(-24)]) / 0.05

PV is approximately $364.48.

In this case, the present value of this ordinary annuity would be approximately $364.48, indicating the current worth of the future cash flows associated with the smartphone payment plan.