Annuity Meaning
Many people have had the experience of making a series of fixed payments over a course of time - such as rent, premium or vehicle payments - or obtaining a series of payments for a course of time, such as the certificate of deposit (CD) or interest from a bond or lending money. These ongoing or recurring payments are technically called "annuities”. Note that there is also a financial product referred to as an annuity, but both are not just similar though the two are related.
Types of Annuities
Annuities, in this sense of the word, are divided into 2 basic types: ordinary annuities and annuities due.
Ordinary Annuities: An ordinary annuity makes (or needs) payments at the termination of each period. For example, bonds usually pay interest at the termination of every 6 months.
Annuities Due: With an annuity due, payments, on the contrary come at the start of each time period. Rent, which landlords typically need at the initiation of each month, is one of the common annuity examples.
How to Calculate Annuities
There are various ways to measure the annuity rate changes or the cost of making such payments or what they're ultimately worth. However, it is first better to know about calculating the present value of the annuity or the future value of the annuity.
Formula to Calculate Present Value Annuities
The formula for the present value of an ordinary annuity:
PV ordinary annuity = P * 1 - (1 + r)-n/ r
Where,
PV = present value of an ordinary annuity
P = value of each payment
R = interest rate/ period
N = total number of periods
The formula for calculating the present value of an annuity due is:
PV Annuity Due = C × [i1 − (1 + i)−n] × (1 + i)
Formula to Calculate Future Value Annuities
Instead of calculating each payment separately and then adding them all up, you can instead apply the following formula, which will tell you the amount of money you'd have in the end:
FV Ordinary Annuity = C × [i(1 + i)n −1]
Where:
C = cash flow/period
i = rate of interest
n = total number of payments
The formula for the future value of an annuity due is:
FV Annuity Due = C × [i(1 + i)n−1] × (1 + i)
Solved Examples
Example:
Calculate the future value of the ordinary annuity and the present value of an annuity due where cash flow per period amounts to rs. 1000 and interest rate is charged at 0.05%.
Solution:
Using the formula to calculate future value of ordinary annuity = C × [(1 + i)n – 1/i
= Rs. 1,000 × [0.05 (1 + 0.05)5−1]
=Rs.1, 000 × 5.53
=Rs. 5,525.63
Note that the one-cent difference in these outcomes, Rs. 5,525.64 vs. Rs. 5,525.63, is because of rounding in the first calculation.
Now to calculate the present value of an annuity due:
Use the formula
PV Annuity Due = C × [i1 − (1 + i)−n] × (1 + i)
Plugging in the values:
= Rs. 1,000 × [0.05(1− (1 + 0.05)−5] × (1 + 0.05)
= Rs. 1,000 × 4.33 × 1.05
= Rs. 4,545.95
Did You Know?
Annuities are applicable when you are saving money.
Generally in an annuity problem, your account begins empty but has money in the future.
Annuities suppose that you put money in the account on a routine basis (every month, quarter year, etc.) and let it remain to earn interest.
If you’re putting money into the account on a regular basis, then you’re looking at a basic annuity problem.
Recurring payments, such as the rent or interest are sometimes referred to as "annuities".
The present value of the annuity is the amount of money that would be needed now to generate those future payments.
The future value of the annuity is the total value of payments at a particular point in time.
In ordinary annuities, payments are released at the end of each time period.
With annuities due, they're made at the commencement of the period.
Conclusion:
The annuity method formula makes it possible - and comparatively easy, - to identify the present or future value of both the ordinary annuity and the annuity due. The future value of the annuity calculator also has the competency to calculate these annuity rate changes for you with the correct inputs.
FAQs on Annuities
1. What is an annuity in simple terms?
In simple terms, an annuity is a series of equal, fixed payments made over a specific period of time at regular intervals. Common examples include monthly rent payments, car loan instalments, or regular deposits into a savings account. It represents a predictable stream of cash flow, either being paid out or received.
2. What are some common real-life examples of annuities?
Annuities are a very common financial concept. Some real-life examples include:
- Loan Repayments: Monthly payments for a car loan or a home mortgage.
- Rent Payments: Paying a fixed amount of rent at the start of every month.
- Insurance Premiums: Regular payments made to an insurance company for coverage.
- Retirement Savings: Regular contributions to a retirement fund like an Employee Provident Fund (EPF) or a Systematic Investment Plan (SIP).
- Retirement Payouts: Receiving a fixed pension every month after retirement.
3. What is the main difference between an ordinary annuity and an annuity due?
The main difference between an ordinary annuity and an annuity due lies in the timing of the payments within each period. An Ordinary Annuity involves payments made at the end of each period (e.g., bond interest payments). In contrast, an Annuity Due involves payments made at the beginning of each period (e.g., rent or insurance premiums).
4. How is the future value (FV) of an annuity calculated?
The Future Value (FV) of an annuity is the total worth of a series of payments at a specific future date, including all the accumulated interest. It tells you how much your regular investments will grow over time. For an ordinary annuity, it is calculated using the formula: FV = P × [((1 + r)^n - 1) / r], where P is the payment amount per period, r is the interest rate per period, and n is the total number of periods.
5. How do you find the present value (PV) of an annuity?
The Present Value (PV) of an annuity is the current worth of a series of future payments, discounted at a specific interest rate. It tells you how much money you would need today to generate those future payments. For an ordinary annuity, the formula is: PV = P × [(1 - (1 + r)^-n) / r], where P is the payment per period, r is the interest rate per period, and n is the number of periods.
6. What are the main types of annuities a student should know?
Annuities can be classified in several ways based on different criteria. The most important types for a student to understand are:
- Based on Payment Timing: This includes the Ordinary Annuity (payments at the end of the period) and the Annuity Due (payments at the beginning).
- Based on Duration: This includes Annuity Certain (payments for a fixed number of years) and Contingent Annuity (payments continue until a specific event occurs, like death).
- Based on Growth: This includes Fixed Annuity (payments are constant) and Growing Annuity (payments increase at a steady rate).
7. Why is it important to distinguish between the present value and future value of an annuity?
Distinguishing between Present Value (PV) and Future Value (FV) is crucial for making sound financial decisions. PV tells you what a future stream of income is worth today, which is essential for determining a fair price for an investment or calculating a loan amount. FV shows you how much your savings or regular investments will be worth in the future, which is fundamental for goal-setting, such as planning for retirement or a child's education.
8. Are annuities considered a type of investment?
Yes, annuities can be a type of investment, particularly when referring to financial products sold by insurance companies. These products are designed to provide a steady income stream, typically during retirement. However, the term 'annuity' in mathematics more broadly describes the structure of any series of regular, fixed payments, which includes both investments (like saving for retirement) and liabilities (like paying off a loan).
9. In what situations would an 'annuity due' be more common than an 'ordinary annuity'?
An annuity due structure is common in situations where a payment is required upfront to secure a service or asset for the upcoming period. Because the payments are made at the beginning of each period, they start earning interest earlier than in an ordinary annuity. Prime examples include:
- Rent payments, which are paid at the start of the month for the right to live in a property for that month.
- Insurance premiums, paid at the beginning of a coverage period to be insured for that duration.
- Lease payments for equipment or property.
10. What is a 'savings annuity' and how does it relate to retirement planning?
A savings annuity refers to a scenario where you make a series of regular deposits to accumulate a larger sum of money for the future. This is the foundational concept behind most retirement planning strategies. For example, contributing a fixed amount from your salary each month to a retirement account like the Public Provident Fund (PPF) or a corporate 401(k) plan is a form of savings annuity. The goal is to use these regular, small contributions to build a substantial fund over many years through the power of compounding interest.
