IB Math AI SL/HL Paper 1 Exam Style Practice Questions: Financial Mathematics

Lesson Overview

In this lesson, we use the TI-84 TVM Solver to model two connected financial situations:

• a savings account growing under compound interest,
• an annuity from which regular monthly withdrawals are made.

Aisha first deposits

into a savings account. After 6 years, the balance has grown to

She then transfers this money into an annuity earning a nominal annual interest rate of

compounded monthly, and withdraws

at the end of each month.

⭐ Key Concepts

• The TVM Solver on the TI-84 is used for loans, savings, and annuities.
• The key fields are:

• For a savings account with no regular payments, use

• For an annuity with monthly withdrawals, withdrawals are entered as negative cash flow if the initial balance is positive.
• Always use consistent sign convention in the TVM Solver.

📘 TI-84 TVM Solver Setup

On the TI-84:

• Press APPS
• Select Finance
• Choose TVM Solver

In IB Mathematics AI, students should clearly show the calculator entries used. In particular, list:

• N
• I%
• PV
• PMT
• FV
• P/Y
• C/Y

Then state which variable is being solved.

📌 Worked Example 1 — Finding the Interest Rate with TVM Solver

Aisha deposits

into a savings account with a nominal annual interest rate of compounded monthly.
At the end of 6 years, the amount has increased to

Find the value of .

Solution

There are 6 years with monthly compounding, so

Now enter the following into the TI-84 TVM Solver:

• N = 72
• I% = ?
• PV = -120000
• PMT = 0
• FV = 168500
• P/Y = 12
• C/Y = 12

Then solve for I%.

The calculator gives

So the nominal annual interest rate is

📊 Marks: M1 A1

📌 Worked Example 2 — Amount Remaining After 9 Years

Aisha withdraws the

and places it into an annuity earning a nominal annual interest rate of

compounded monthly. At the end of each month, she withdraws

Find the amount of money remaining in the annuity at the end of 9 years.

Solution

There are 9 years with monthly withdrawals, so

Enter the following into the TI-84 TVM Solver:

• N = 108
• I% = 5.4
• PV = 168500
• PMT = -1350
• FV = ?
• P/Y = 12
• C/Y = 12

Then solve for FV.

The calculator gives

So the amount remaining after 9 years is

📊 Marks: M1 A1

📌 Worked Example 3 — Number of Full Monthly Withdrawals

Determine how many full monthly payments of $1350 Aisha can receive before the annuity is exhausted.

Solution

To find how many full payments can be made, set the final value to zero.

Enter the following into the TI-84 TVM Solver:

• N = ?
• I% = 5.4
• PV = 168500
• PMT = -1350
• FV = 0
• P/Y = 12
• C/Y = 12

Then solve for N.

The calculator gives

This means Aisha can receive

full monthly payments of $1350 before the annuity is exhausted.

📊 Marks: M1 A1

⚠ Common Mistakes

• Forgetting to use P/Y = 12 and C/Y = 12 for monthly payments and monthly compounding.
• Entering the cash flow signs incorrectly in the TVM Solver.
• Using the 6-year balance as a payment instead of as the present value of the annuity.
• Rounding the interest rate too early and then getting a different final balance.
• For part (c), giving 184 payments instead of the number of full payments.

📘 IB Exam Tips

• In AI, always list the TVM Solver entries clearly before stating the answer.
• Use PMT = 0 for pure compound growth questions with no regular deposits or withdrawals.
• Use FV = 0 when finding how long an annuity lasts until it is exhausted.
• When solving for the number of payments, interpret the calculator output carefully if it is not an integer.
• Keep full calculator accuracy until the end, then round monetary answers to 2 decimal places.

Noah deposits

into a savings account with a nominal annual interest rate of compounded monthly.
After 5 years, the balance is

He then transfers this amount into an annuity earning

nominal annual interest compounded monthly, and withdraws

at the end of each month.

(a) Use the TI-84 TVM Solver to find .

(b) Use the TI-84 TVM Solver to find the amount remaining after 8 years.

(c) Use the TI-84 TVM Solver to determine how many full monthly payments Noah can receive before the annuity is exhausted.

Maya deposits

into a savings account with nominal annual interest rate compounded monthly.
After 4 years, the amount is

She then places this money into an annuity earning

nominal annual interest compounded monthly, and withdraws

at the end of each month.

(a) Use the TI-84 TVM Solver to find .

(b) Use the TI-84 TVM Solver to find the amount remaining after 7 years.

(c) Use the TI-84 TVM Solver to determine how many full monthly payments Maya can receive before the annuity is exhausted.