# BM9.2 – Working with Lump-Sums Chapter 9, Lesson 2

In this lesson students will:

• solve annuity problems involving opening balances by hand and using the calculator
• solve annuity problems involving a final lump-sum payment by hand and using the calculator

## Lump-Sums

In our previous chapters, we have focused our discussion on annuities in which either (1) we calculate the future value and assume the principle amount is zero, or (2) calculate the principle amount and assume the principle amount is zero. However, in practice, this might not always be the case. For instance, we might open up an RRSP account by first depositing an initial amount, then make regular payments to top the account up. In another instance, we may borrow a loan and make regular payments; and when we reach a certain remaining balance we pay the loan off in full. We refer to both of these cases as working with lump-sums, and we will divide this lesson into two parts: lump-sums as an opening balance, and lump-sums as a final payment.

#### Opening Balances

Consider the scenario in which you wish to open an RRSP account and make month-end payments of $\ 250$ for the next five years. Let’s assume the account earns $3.75\%$ compounded monthly. However, you have recently moved jobs, and would like to move the $\150,740$ you have saved up there and use it as an initial deposit in your new account. What will be the total balance in your account five years from today? Let’s solve this question in the following video both by hand, and using the TI BA II Plus calculator.

#### Final Payments

Consider the scenario in which you take out a loan and pay it off by making equal-sized payments of $\500$ at the beginning of every month for five years. After your last payment at the five-year mark, there is $\1200$ left to pay, so you decide to do this by making one final lump-sum payment. If the interest on your loan is $3\%$ compounded weekly, how much did you initially borrow from the bank? Let’s solve this question in the following video both by hand, and using the TI BA II Plus calculator.