# Future Value of Annuity Due Formula

The future value of an annuity due is the value of consolidated payments at a date in the future, considering a fixed return or discount rate. Annuity’s future value increases with the increase in the discount rate.

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## 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%.

 Number of periodic payments in a year 12 Monthly Payment (P) Rs 2,000/- The effective rate of Interest ( r ) 0.42% Number of Periods ( n ) 48

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.

## FAQ's

• ### Q. What is the relevance of the future value of an annuity due?

Ans. The future value of annuity due is a parameter of the time value of money. Your money can grow as time passes by.
• ### Q. Where is the future value of annuity due used?

Ans. The future value of an annuity due is used at several instances, for example:
• To calculate the premium for life insurance.
• For calculation of provident fund in the case where the monthly contribution acts as a periodic payment.
• ### Q. What is the correlation between the discount rate and the future value of an annuity?

Ans. Based on the discount rate, the future value grows. Thereby, it is inferred that the higher the discount rate, the higher the future value of the annuity.
• ### Q. What is an annuity due?

Ans. Annuity refers to a series of equal payments that are made at periodical intervals at the beginning of the period. The period can be monthly, quarterly, semi-annually, or annually.
• ### Q. What is the present value of an annuity due?

Ans. Under the present value of annuity due, the cash flows are discounted to time zero. The formula used is
PV of annuity due = PMT * 1 - (1 + r) - n * (1 + r) / r
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