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Future Value of Annuity

Delve into the compelling world of Corporate Finance with an in-depth exploration of the Future Value of annuity in business studies. Grasp its definition, importance in corporate finance, and learn how to accurately calculate it. Unravel the intricacies of the future value of annuity formula, using clear step-by-step explanations and…

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Jetzt kostenlos anmeldenDelve into the compelling world of Corporate Finance with an in-depth exploration of the Future Value of annuity in business studies. Grasp its definition, importance in corporate finance, and learn how to accurately calculate it. Unravel the intricacies of the future value of annuity formula, using clear step-by-step explanations and real-life examples. Finally, gain insights into future value of annuity tables and the concept of future value of a growing annuity. This comprehensive guide is essential for any budding business student keen to develop their understanding of this vital financial tool.

The Future Value of Annuity (FVA) is the estimated total amount that a sequence of equal payments or investments will be worth at a future date, as they grow with interest compounded at a specific rate.

- \(P\) is the payment or investment made in each period
- \(r\) is the interest rate per period
- \(n\) is the total number of periods

Application | Description |

Financial Planning | Helps firms estimate the future value of constant cash flows, aiding in creating accurate financial strategies. |

Retirement Plans | Used in determining the future worth of equal contributions made towards a retirement fund or any similar investment plan. |

Loan Repayments | Used by banks and other financial institutions to estimate the total repayment from an annuity loan. |

Knowing the Future Value of Annuity can assist businesses in making strategic decisions. For instance, knowing the FVA of a pension fund can help companies plan and fund their employee pension schemes effectively.

Consider a company that invests £5000 every year for ten years in an account that offers a 5% interest rate compounded annually. The Future Value of Annuity would then be calculated as: \( FVA = £5000 \times \left( \frac{(1 + 0.05)^{10} - 1}{0.05} \right) = £66,033.96 \) Thus, at the end of ten years, the total amount in the account would be £66,033.96. This kind of calculation helps the company plan its finances better.

**\(P\)**stands for the payment or investment made in each period. This is the amount consistently deposited or invested at scheduled intervals. For instance, if you invest £1000 monthly into a saving account, then \(P = £1000\).**\(r\)**represents the interest rate per period. This is the rate at which your investment grows during each period, usually given as a percentage. If your savings account grows at a rate of 5% annually, then \(r = 0.05\).**\(n\)**is the total number of periods. This refers to the number of times the investment is made over the lifespan of the annuity. If you're investing £1000 every year for five years, then \(n = 5\).

Step 1: Identify \(P\), \(r\), and \(n\) from the problem statement. Step 2: Substitute these identified values into the Future Value of Annuity formula. Step 3: Compute the expression within the parentheses. This calculates the amount your annuity would grow due to compound interest. Step 4: Finally, multiply this result by \(P\), the periodic payment, to find the Future Value of Annuity.For instance, let's say you invest £2000 each year into an account with a fixed annual interest rate of 3% for a total of 10 years. To find the Future Value of Annuity, you'd use the values \(P = £2000\), \(r = 0.03\), and \(n = 10\), plug them into the formula, and execute the steps as instructed.

Given, \(P = £2000\), \(r = 3\% = 0.03\), and \(n = 10\) years. Using the Future Value of Annuity Formula, \( FVA = £2000 \times \left( \frac{(1 + 0.03)^{10} - 1}{0.03} \right) \) Solving the bracket term first, \( FVA = £2000 \times \left( \frac{1.344 - 1}{0.03} \right) = £22933.35 \) Therefore, the Future Value of Annuity is £22933.35.

- \(P\) is the regular investment or payment
- \(r\) is the interest rate per period
- \(n\) is the number of periods

While this might seem straightforward, it's important to remember that the power of compounding can dramatically increase the Future Value of Annuity. Do not underestimate the impact of consistent payments and a reliable interest rate over time.

1 | 2 | 3 | ... | |

1% | 1.01 | 2.0301 | 3.0604 | ... |

2% | 1.02 | 2.0404 | 3.0612 | ... |

... | ... | ... | ... | ... |

10% | 1.1 | 2.21 | 3.31 | ... |

- Future Value of Annuity (FVA) is a crucial corporate finance tool that helps in financial planning, estimating future loan repayments, planning retirement funds and making strategic business decisions.
- The Future Value of Annuity formula calculates the total value of a sequence of equal payments at a certain point in the future, given an interest rate: FVA = P * [(1 + r)^n - 1]/r.
- Within the formula, \(P\) represents the payment or investment made in each period, \(r\) represents the interest rate per period, and \(n\) is the total number of periods. The formula accounts for the cumulative effect of compound interest.
- Before calculating the Future Value of Annuity, understanding of the concept of annuity, interest rates, and the process of compounding is necessary. Annuity is a series of equal payments made at regular intervals.
- To consistently calculate the Future Value of Annuity, identify \(P\), \(r\), and \(n\) from your problem statement, substitute these values into the formula and calculate the expression within the parentheses. Multiply this result by \(P\) to find the FVA.
- Future Value of Annuity tables and the concept of growing annuity provide further insight on how annuity payments can grow over time. FVA tables show the future values of an ordinary annuity for different combinations of interest rates and periods.

The future value of an annuity can be calculated using the formula FV = P * [(1 + r)^nt - 1] / r, where FV is the future value, P is the annuity payment, r is the interest rate per period, n is the number of times interest is compounded per period, and t is the time in years.

The future value annuity factor is a formula used to calculate the future value of a series of cash flows, or annuities. It considers both the number of periods and the periodic interest rate to determine the total value at the end of the investment or payment period.

The formula for future value of an annuity due is: FV = P * [(1 + r)^t - 1] / r * (1 + r), where 'FV' represents future value, 'P' stands for payment per period, 'r' is the interest rate, and 't' signifies the number of periods.

The present value of an annuity represents how much its periodic payments are worth in today's money, while the future value of an annuity indicates what total value those payments will accumulate to at a specific point in the future, considering compounding interest.

As time increases, the future value of an annuity also increases. This is because the longer the time period, the more interest compounds, leading to a higher future value.

Flashcards in Future Value of Annuity15

Start learningWhat is the Future Value of Annuity (FVA) in Business Studies?

The FVA is the estimated total amount that a sequence of equal payments or investments will be worth at a future date, as they grow with interest compounded at a specific rate.

What is the formula for calculating the Future Value of Annuity (FVA)?

The formula for FVA is P x ((1 + r)^n - 1) / r, where P is the payment or investment made each period, r is the interest rate per period, and n is the number of periods.

How is the Future Value of Annuity (FVA) used in Corporate Finance?

The FVA is used for financial planning, estimating future value of constant cash flows, determining the future worth of retirement plans, and estimating total repayment from annuity loans.

What is the Future Value of Annuity (FVA) formula and what does it help calculate?

The Future Value of Annuity (FVA) formula is \(FVA = P \times \left( \frac{(1 + r)^n - 1}{r} \right)\). It helps to calculate the total value of a sequence of equal payments (an annuity) at a specific point in the future, considering interest compounding at a specific rate.

What do the variables \(P\), \(r\), and \(n\) represent in the FVA formula?

\(P\) represents the payment or investment made each period, \(r\) is the interest rate per period and \(n\) is the total number of periods.

What are the steps involved in applying the Future Value of Annuity formula?

Steps involve: 1) Identifying the values of \(P\), \(r\), and \(n\), 2) Substituting these values into the formula, 3) Computing the expression in parentheses (calculating the effect of compound interest), and 4) Multiplying the result by \(P\) to find the Future Value of Annuity.

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