Future Value of Annuity Due Formula

Formula: 

The formula for calculating the future value of annuity due is: 

FVA Due = P * {(1 + r) n - 1) * (1 + r) / r}, 

Where, 

FVA denotes Future Value of Annuity 

P denotes Periodic Payment

n denotes Number of Periods

r denotes Effective interest rate 

To elaborate further, let us understand the same through some examples:

Mr. A decides to deposit a monthly payment of Rs 2,000/- for the next four years at the beginning of each month. The ongoing interest rate being charged by the bank is 5%. 

Future value of Annuity Due = 2,000 * {(1 + 0.42%) 48 - 1} * (1 + 0.42%) / 0.42% = Rs 1,06,472/-.  

Mr. B plans to deposit Rs 5,000/- at the beginning of each year for 7 years. The ongoing rate of interest in the market is 5%. 

The FV of Annuity Due = P * {(1 + r) n - 1} * (1 + r) / r

= 5000 * {1 + 5%) 7 - 1} * (1 + 5%) / 5% = Rs 42,746/-. 

The following steps are to be followed: 

• Determine the amount that is to be paid in each period. The payments should be equal to periodic payments. They are referred to as P. 

• Next, find out the interest rate charged based on the rates prevalent in the market. It is denoted by r. 

• The formula to calculate r i.e. annualized rate of Interest/ number periodic payments in a year. 

• It is the interest rate to be received by the investor when the money is invested in the market. 

• After which, the total number of periods is derived by multiplying the number of years with the number of periodic payments, i.e., n = Number of years * Number of periodic payments in a year. 

• Then, the future value of an annuity can be calculated using the formula stated above.        

How Is the Formula for Future Annuity Due Derived?

In the first alternative, FV = PV (1 + r) n, i.e., you can multiply (1 + r) n by the current value of annuity due. The formula for current value of annuity due is (1 + r) * P {1 - (1 + r) - n} / r.    

 The second method is to make a comparison between the cash movements in an annuity due and an ordinary annuity.

• For an annuity due = P (1 + r) + P (1 + r) 2 ………. P (1 + r) n

• For an ordinary annuity = P + P (1 + r) ………P (1 + r) n - 1

The annuity due cash flow becomes equivalent to the ordinary cash flow when (1 + r) is factored.   

In Conclusion

The formula used is quick, easy to comprehend, and useful to the user at multiple stages in life.

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