# BM9.3 – Working with Multiple Annuities

Chapter 9, Lesson 3

In this lesson students will:

• determine the future value or principle amount of a payment stream involving the addition of two annuities
• determine the future value or principle amount of a payment stream involving the subtraction of two annuities

## Working with Additional Payments

In the first part of this lesson, we will work with examples involving payment streams in which some equal size payments might be larger than others. It is possible to solve these problems using the formulas; however, we will focus on using the TI BA II Plus calculator. The main strategy when working with additional payments is to break the question up into two annuity calculations, then add them up to obtain the final answer.

Consider the following example: You deposit $\500$ at the end of every month for the next ten years into a bank account that can earn $5\%$ compounded weekly. At the end of every year, you decide to deposit an additional $\400$ ($\900$ in total). Determine the future value of the account ten years from today.

Consider the following example: Determine the fair market value today of a payment stream that pays $\1500$ at the beginning of every week, with an additional payment of $\1000$ at the beginning of every month, for three years if money can earn $2.5\%$ compounded monthly.

## Working with Missing Payments

In the second part of this lesson, we will consider cases of payment streams in which we regularly skip a payment. Once again, we will focus on how to use the TI BA II Plus calculator to solve these problems. The main strategy when working with missing payments is to break the question up into two annuity calculations, then subtract them to obtain the final answer.

Consider the following example: You deposit $\800$ at the end of every month for the next seven years into a bank account that can earn $3\%$ compounded bi-weekly. At the end of every year, however, you decide to skip the payment. Determine the future value of the account seven years from today.

Consider the following example: Determine the fair market value today of a payment stream that pays $\1000$ at the beginning of every month, with a skipped at the beginning of every quarter, for four years if money can earn $4.5\%$ compounded monthly.