How to Calculate an Annuity Due on a Financial Calculator

An annuity due represents a series of equal payments made at regular intervals, with each payment occurring at the beginning of the period. This financial arrangement is common in scenarios such as lease payments, rent, and insurance premiums, where funds are typically required upfront. This article guides readers through calculating an annuity due using a financial calculator.

Understanding Annuity Due Fundamentals

An annuity due differs from an ordinary annuity by the timing of its payments. In an annuity due, payments are made at the start of each period, allowing funds an additional period to earn interest. An ordinary annuity involves payments made at the close of each period. This timing difference influences the present and future values of the annuity.

Annuity calculations use several key variables. “N” signifies the total number of payment periods. “I/Y” stands for the interest rate per period, which is the rate at which the annuity’s value grows or discounts. “PMT” denotes the fixed payment amount made or received in each period.

“PV” refers to the present value, the current worth of a future stream of payments. “FV” represents the future value, indicating the accumulated worth of payments at a specified future point.

Setting Up Your Financial Calculator

Before performing annuity due calculations, clear your financial calculator’s previous data to prevent errors. For Texas Instruments BA II Plus, press “2nd” then “FV” (CLR TVM). On an HP 12c, press “f” then “x⇔y” or “f” then “CLR FIN”.

Switch the calculator’s payment mode from the default “END” (for ordinary annuities) to “BEGIN” mode. For the TI BA II Plus, press “2nd” then “BGN” (above PMT), then “2nd” followed by “SET”. The display should show “BGN”. For an HP 12c, press “g” then “7”; “BEGIN” will appear.

Ensure the “payments per year” (P/Y) and “compounding periods per year” (C/Y) settings align with the payment frequency. For monthly payments, set both to 12. On the TI BA II Plus, access this by pressing “2nd” then “I/Y” (P/Y), entering the number, pressing “ENTER,” then “2nd” and “QUIT”. The HP 12c handles this through its interest rate input, where the rate corresponds to the period’s frequency.

Performing Annuity Due Calculations

Once your financial calculator is set to “BEGIN” mode, you can perform annuity due calculations. Enter PMT values as negative for cash outflows (payments made) and positive for inflows (payments received). Consistent sign convention ensures accurate results.

Calculating the Present Value of an Annuity Due

To determine the present value (PV) of an annuity due, consider receiving $500 at the beginning of each month for 5 years, with an annual interest rate of 6%. Ensure your calculator is in “BEGIN” mode and cleared. For the TI BA II Plus, input “60” for N (5 years 12 months), “0.5” for I/Y (6% annual / 12 months), and “500” for PMT. Then, press “CPT” followed by “PV”.

For an HP 12c, after setting to “BEGIN” mode and clearing memory, enter “60” then “n”, “0.5” then “i”, and “500” then “PMT”. Press “PV” to calculate the present value. This value represents the lump sum needed today to generate that series of future payments, useful for evaluating investments or determining the cost of future receipts.

Calculating the Future Value of an Annuity Due

To calculate the future value (FV) of an annuity due, imagine investing $200 at the beginning of each month for 10 years, earning an annual interest rate of 3%. With your calculator in “BEGIN” mode and memory cleared, for the TI BA II Plus, input “120” for N (10 years 12 months), “0.25” for I/Y (3% annual / 12 months), and “-200” for PMT. Then, press “CPT” followed by “FV”.

For an HP 12c, after confirming “BEGIN” mode and clearing memory, enter “120” then “n”, “0.25” then “i”, and “-200” then “PMT”. Press “FV” to obtain the future value. This result shows the total accumulated amount at the end of the period, including all payments and compounded interest. This calculation is valuable for retirement planning or savings goals.

Calculating the Payment (PMT) of an Annuity Due

To determine the required payment (PMT) for an annuity due, consider a $10,000 loan over 3 years with monthly payments at an annual interest rate of 4.8%, due at the beginning of each month. For the TI BA II Plus in “BEGIN” mode, input “36” for N (3 years 12 months), “0.4” for I/Y (4.8% annual / 12 months), and “10000” for PV. Then, press “CPT” followed by “PMT”.

For an HP 12c, ensure “BEGIN” mode is active and memory is clear. Enter “36” then “n”, “0.4” then “i”, and “10000” then “PV”. Press “PMT” to calculate the monthly payment. This method also applies if saving for a future goal, such as accumulating $50,000 in 15 years with monthly deposits at the beginning of each month, at an annual interest rate of 3.6%. For this, input “50000” as FV and compute PMT.