Future Value of Annuity Explained.

Описание: In this video, we explain future value of annuity.

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Future Value of Annuity: An Overview
The Future Value (FV) of an annuity refers to the value of a series of periodic payments or receipts at a specific point in the future, considering a certain interest rate or rate of return. An annuity can be regular (with payments made at the end of each period) or annuity due (with payments made at the beginning of each period). The future value helps determine how much an investor will accumulate at the end of the annuity period based on the payment schedule and interest rate.

Formula for Future Value of Annuity
The general formula for calculating the future value of an ordinary annuity (where payments are made at the end of each period) is:

FV=P× r(1+r) n −1/r
​
Where:
FV = Future Value of the annuity
P = Periodic payment (deposit or withdrawal)
r = Interest rate per period
n = Number of periods (total payments)
For an annuity due (where payments are made at the beginning of each period), the formula adjusts to:

𝐹𝑉due=𝐹𝑉ordinary×(1+𝑟)FV
due
​
Where FVₒrₑₓₖ is the future value of an ordinary annuity.

Example: Future Value of an Ordinary Annuity
Let’s assume:

A person invests $1,000 at the end of each year for 5 years.
The interest rate is 6% per year.
Using the formula:

𝐹𝑉=1,000×(1+0.06)5−1/0.06
𝐹𝑉=1,000×(1.3382)−1/0.06

𝐹𝑉=1,000×0.3382/0.06
FV=1,000×5.6367=5,636.71

So, the future value of the annuity is $5,636.71.

Example: Future Value of an Annuity Due
If the payments are made at the beginning of each period (annuity due), the future value is adjusted as follows:

𝐹𝑉due=5,636.71×(1+0.06)=5,636.71×1.06=5,969.91
The future value of an annuity due would be $5,969.91, which is slightly higher because the interest is calculated for one additional period.

Important Considerations
Payment Frequency: If payments are made more frequently than annually, adjust the interest rate and number of periods to match the payment frequency (e.g., monthly payments require dividing the interest rate by 12 and multiplying the number of years by 12).

Time Value of Money: The future value of an annuity incorporates the concept of the time value of money, which acknowledges that money has the potential to earn interest over time.

Compounding Period: The future value calculation assumes interest is compounded regularly (annually, monthly, etc.). The more frequent the compounding, the higher the future value of the annuity will be.

Applications of Future Value of Annuity
Retirement Planning: Estimating how much a person will accumulate in a retirement account based on regular contributions.
Loan Repayments: Calculating the total amount that will be paid over time for a loan that involves regular installments.
Investment Growth: Understanding how an investment will grow over time with regular contributions or withdrawals.

Conclusion
The future value of an annuity helps individuals and businesses assess the outcome of regular payments made or received over time, considering the time value of money. By adjusting the formula for different payment frequencies or payment timings (ordinary annuity or annuity due), one can accurately forecast the future worth of such financial arrangements.

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