Annuity Due Calculations: Financial Analysis and Examples

Understanding Annuity Due

An annuity due is a series of equal payments made at the beginning of each period. Below are practical examples to help you master these calculations.

Example 1: Lease vs. Cash Purchase

You are buying a new vehicle and must decide between leasing or paying cash. The salesperson offers a cash price of $23,000 or a five-year lease with:

• Monthly payments of $300 (first payment due at signing).
• A buyout of $9,500 at the end of five years.

Since the first payment is made at the start, the lease requires 59 additional equal payments. Assuming a 6% annual interest rate compounded monthly (0.5% per month):

• BGN Mode: N = 60, I = 0.5, FV = $9,500, PMT = $300
• Result: CPT PV = –$22,638

Conclusion: The lease is the better deal because the present value (PV) is lower than the cash price.

Example 2: Future Value of an Annuity Due

Find the Future Value (FV) of payments of $1,000 made at the beginning of each year for 3 years at 5% interest compounded annually.

• Settings: BGN, P/Y = 1, C/Y = 1 (Simple Annuity Due)
• Calculation: PMT = 1,000, N = 3, I/Y = 5
• Result: FV = $3,310.13

Example 3: General Annuity Due

A four-year lease requires payments of $10,000 at the beginning of every year. If the interest rate is 6% compounded monthly, what is the cash value?

• Settings: BGN, P/Y = 1, C/Y = 12 (General Annuity Due)
• Calculation: PMT = 10,000, N = 4, I/Y = 6
• Result: PV = $36,647.36

Example 4: Monthly Deposit Accumulation

What monthly deposit made at the beginning of each month will accumulate to $120,000 at 8% compounded semi-annually over 10 years?

Result: $656.40

Example 5: Time Required to Reach a Goal

Laura wants to accumulate $150,000 by depositing $1,000 at the beginning of each month. If the account earns 5% compounded quarterly, how long will it take?

Result: n = 116.5 months (approx. 9.7 years)

Example 6: Multi-Stage Savings Growth

James deposited $150 at the beginning of each month for two years. For the next four years, he made no further deposits. With 4% interest compounded monthly, what is the balance after 12 years?

Result: $4,404.70

Hint: First, calculate the FV after 2 years. Use that amount as the Present Value for the remaining years using the compound interest formula.