Formula to Calculate Future Value of Annuity Due
Future value of annuity due is value of amount to be received in future where each payment is made at the beginning of each period and formula for calculating it is the amount of each annuity payment multiplied by rate of interest into number of periods minus one which is divided by rate of interest and whole is multiplied by one plus rate of interest.
The term “future value of an annuity” refers to the future value of the string of consecutive and equal payments that are likely to be made in the future. Further, annuity due indicates that the payments are done at the beginning of the time period. The formula for the future value of an annuity due is calculated based on periodic payment, number of periods and effective rate of interest. Mathematically, it is represented as,
where FVA Due = Future value of an annuity due
- P = Periodic payment
- n = Number of periods
- r = Effective rate of interest
How to Calculate Future Value of Annuity Due? (Step by Step)
The formula to calculate the future value of an annuity due can be derived by using the following steps:
- Step 1: Firstly, figure out the payments that are to be paid in each period. Please keep in mind that the above formula is applicable only in the case of equal periodic payments It is denoted by P.
- Step 2: Next, figure out the rate of interest to be charged on the basis of the prevalent market rate. It is the rate of interest to be received by the investor if the money is invested in the market. To get an effective rate of interest, divide the annualized rate of interest by the number of periodic payments in a year. It is denoted by r. i.e r = Annualized rate of interest / Number periodic payments in a year
- Step 3: Next, the total number of periods is computed by multiplying the number of periodic payments in a year and the number of years. It is denoted by n. i.e n = Number of years * Number of periodic payments in a year
- Step 4: Finally, the future value of an annuity due is calculated based on periodic payment (step 1), effective rate of interest (step 2) and a number of periods (step 3) as shown above.
Let us take the example of John Doe who plans to deposit $5,000 at the beginning of each year for the next seven years to save enough money for his daughter’s education. Determine the amount that John Doe will have at the end of seven years. Please note that the ongoing rate of interest in the market is 5%.
Calculate the FV of annuity due for the Periodic Payment using above given information,
FV of Annuity Due = P * [(1 + r)n – 1] * (1 + r) / r
= $5,000 * [(1 + 5%)7 – 1] * (1 + 5%) / 5%
Future Value of Annuity Due will be –
= $42,745.54 ~ $42,746
Therefore, after seven years John Doe will have $42,746 to spend for his daughter’s education.
Let us take another example of Nixon’s plans to accumulate enough money for his MBA. He decides to deposit a monthly payment of $2,000 for the next four years (beginning of each month) so that he is able to gather the required amount of money. As per the education counselor, Nixon will require $100,000 for his MBA. Check if Nixon’s deposits will fund his plans for an MBA considering the ongoing rate of interest being charged by a bank is 5%.
- Monthly payment, P = $2,000
- Effective rate of interest, r = 5% / 12 = 0.42%
- Number of periods, n = 4 * 12 months = 48 months
Calculate the FV of Annuity Due for monthly payment using the above given information,
= $2,000 * [(1 + 0.42%)48 – 1] * (1 + 0.42%) / 0.42%
Future value of Monthly Payment will be –
FV of Annuity Due = $106,471.56 ~ $106,472
So, with planned deposits, Nixon is expected to have $106,472 which more than the amount ($100,000) required for his MBA.
Relevance and Uses
The future value of an annuity due is another expression of the time value of money, the money received today can be invested now that will grow over the period of time. One of the striking applications of the future value of an annuity due is in the calculation of the premium payments for a life insurance policy. It also finds application in the calculation of provident fund where the monthly contribution from the salary acts as the periodic payment. The future value of annuity grows based on the stated discount rate, as such the higher discount rate the higher will be the future value of the annuity.
This has been a guide to the Future Value of Annuity Due Formula. Here we learn how to calculate the future value of an annuity due using its formula along with some practical examples and downloadable excel template. You may learn more about Financial Modeling from the following articles –