How Do You Calculate the Value of an Annuity?

You calculate an annuity’s value in IB Mathematics: Applications and Interpretation using the finance solver on your GDC. Enter the payment schedule, interest rate, and known values, then solve for either the present value or future value.

Choosing the Value

An annuity consists of equal payments made at regular intervals. Under the IB examination convention, payments occur at the end of each period.

Using the Finance Solver

Enter these variables:

• $N$: total number of payments
• $I\%$: annual nominal interest rate
• $PV$: present value
• $PMT$: regular payment
• $FV$: future value
• (P/Y): payments per year
• (C/Y): compounding periods per year

First match every input to the same time structure. For example, five years of monthly payments gives $N=5\times12=60$, while monthly payments and monthly compounding normally require $P/Y=C/Y=12$.

Cash paid out and cash received must have opposite signs. This is the cash-flow sign convention.

Worked Example

A student deposits 200 dollars at the end of every month for five years into an account paying $4.8\%$ annual interest, compounded monthly.

Use the finance solver:

$$N=60,\quad I\%=4.8,\quad PV=0,\quad PMT=-200,\quad P/Y=C/Y=12$$

Solving for $FV$ gives:

$$FV=13\,532.04$$

Therefore, the annuity will be worth 13,532.04 dollars after five years. The deposits total $60\times200=12\,000$ dollars, so the remaining $1\,532.04$ dollars represents interest earned. Keep the full GDC value during calculations and round money only at the end.

Exam Technique

This is SL 1.7, Loan repayments and amortization and may appear on either GDC-active Paper 1 or Paper 2. The annuity formula is not examined; show the finance-solver variables because they provide evidence of method. A common misconception is entering both $PMT$ and $FV$ with the same sign, which usually produces an error or an incorrect interpretation.