- Introduction - Time Value of Money
- Interest Rates
- Interest Rate Equation
- Nominal Interest Rate and Effective Yield
- Time Value of Money for Different Compounding Frequencies
- Future Value of a Single Cash Flow
- Present Value of a Single Cash Flow
- Future Value and Present Value of Ordinary Annuity
- Present Value and Future Value of Annuity Due
- Present Value of a Perpetuity
- Present Value and Future Value of Uneven Cash Flows
- Annuities with Different Compounding Frequencies
- Using a Timeline to Solve Time Value of Money Problems

# Annuities with Different Compounding Frequencies

In all the above examples for annuities, we assumed that the compounding frequency is annual. However, this may not always be the case and an annuity may have monthly, quarterly, or even semi-annual compounding. We can solve the time value of money problems for any of these compounding frequencies using the BA II Plus calculator.

Let’s take an example. An ordinary annuity pays $250 every quarter for the next 5 years. The expected rate of return is 8% per annum. Calculate the present value of this annuity.

We can solve this problem using two methods.

**Method 1:**

Since payments are made quarterly, change the number of payments per year to 4. Press [2ND][P/Y]. Input 4 and then press ENTER.

Now enter the following values for variables.

N=20 (20 quarters in 5 years)

I/Y = 8 (Interest rate per annum)

PMT = $250

Then compute the Present Value [CPT][PV].

PV = $4087.85

**Method 2**

Keep the number of periods per as 1 (Annual Compounding).

Enter the following variables:

N=20 (20 quarters in 5 years)

I/Y = 2% (Annual interest rate /4)

PMT = $250

Then compute the Present Value [CPT][PV].

PV = $4087.85

Both the methods are accurate and produce the same result. Try both methods and follow the one you are more comfortable with. One problem in the first method is that you will have to change the compounding frequency (P/Y) and then reset it after you have solved the problem.

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