The term annuity is used in finance theory to refer to any terminating stream of fixed payments over a specified period of time. This usage is most commonly seen in discussions of finance, usually in connection with the valuation of the stream of payments, taking into account time value of money For example, 100 dollars of today's money invested for one year and earning 5 percent interest will be worth 105 dollars after one year. Therefore, 100 dollars paid now or 105 dollars paid exactly one year from now both have the same value to the recipient assuming 5 percent interest; using time value of money terminology, 100 dollars invested for concepts such as interest rate An interest rate is the price a borrower pays for the use of money they borrow from a lender, for instance a small company might borrow capital from a bank to buy new assets for their business, and the return a lender receives for deferring the use of funds, by lending it to the borrower. Interests rates are fundamental to a Capitalist society[ and future value Future value measures the nominal future sum of money that a given sum of money is "worth" at a specified time in the future assuming a certain interest rate, or more generally, rate of return; it is the present value multiplied by the accumulation function.[1]
Examples of annuities are regular deposits to a savings account, monthly home mortgage payments and monthly insurance payments. Annuities are classified by payment dates. The payments (deposits) may be made weekly, monthly, quarterly, yearly, or at any other interval of time.
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Ordinary annuity
An ordinary annuity (also referred as annuity-immediate) is an annuity whose payments are made at the end of each period (e.g. a month, a year). The values of an ordinary annuity can be calculated through the following:[2] An annuity calculator can help you figure out the fixed payments you'll receive over time. The calculator uses the initial principal balance, the interest rate received, and the length of the payment schedule period to calculate annuity payments [3].
Let:
- r = the yearly nominal interest rate In finance and economics nominal interest rate or nominal rate of interest refers to the rate of interest before adjustment for inflation ; or, for interest rates "as stated" without adjustment for the full effect of compounding (also referred to as the nominal annual rate). An interest rate is called nominal if the frequency of.
- t = the number of years.
- m = the number of periods per year.
- i = the interest rate per period.
- n = the number of periods.
Note:
- n = tm
Also let:
- P = the principal (or present value).
- S = the future value of an annuity.
- R = the periodic payment in an annuity (the amortized payment).
Also:
Clearly, in the limit as n increases,
Thus, even an infinite series of finite payments (perpetuity A perpetuity is an annuity that has no definite end, or a stream of cash payments that continues forever. There are few actual perpetuities in existence (the United Kingdom government has issued them in the past; these are known and still trade as consols). A number of types of investments are effectively perpetuities, such as real estate and) with a non-zero discount rate has a finite present value.
Proof
The next payment is to be paid in one period. Thus, the present value is computed to be:
- .
We notice that the second term is a geometric progression In mathematics, a geometric progression, also known as a geometric sequence, is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed non-zero number called the common ratio. For example, the sequence 2, 6, 18, 54, ... is a geometric progression with common ratio 3. Similarly 10, 5, 2.5, 1.25, .. of scale factor 1 and of common ratio . We can write
- .
- .
Similarly, we can prove the formula for the future value. The payment made at the end of the last year would accumulate no interest and the payment made at the end of the first year would accumulate interest for a total of (n−1) years. Therefore,
- .
Hence:
- .
Additional formula
If an annuity is for repaying a debt P with interest, the amount owed after n payments is:
because the scheme is equivalent with lending an amount and putting part of that, an amount , in the bank to grow due to interest. See also fixed rate mortgage A fixed rate mortgage is a mortgage loan where the interest rate on the note remains the same through the term of the loan, as opposed to loans where the interest rate may adjust or "float." Other forms of mortgage loan include interest only mortgage, graduated payment mortgage, variable rate (including adjustable rate mortgages and.
Annuity-due
An annuity-due is an annuity whose payments are made at the beginning of each period.[4] Deposits in savings, rent payments, and insurance premiums are examples of annuities due.
Because each annuity payment is allowed to compound for one extra period, the value of an annuity-due is equal to the value of the corresponding ordinary annuity multiplied by (1+i). Thus, the future value of an annuity-due can be calculated through the formula (variables named as above):[5]
It can also be written as
- (1 + i)
An annuity-due with n payments is the sum of one annuity payment now and an ordinary annuity with one payment less, and also equal, with a time shift, to an ordinary annuity with one payment more, minus the last payment.
Thus we have:
- (value at the time of the first of n payments of 1)
- (value one period after the time of the last of n payments of 1)
Other types
- Fixed annuities – These are annuities with fixed payments. They are primarily used for low risk investments like government securities or corporate bonds. Fixed annuities offer a fixed rate but are not regulated by the Securities and Exchange Commission The U.S. Securities and Exchange Commission is an independent agency of the United States government which holds primary responsibility for enforcing the federal securities laws and regulating the securities industry, the nation's stock and options exchanges, and other electronic securities markets. The SEC was created by section 4 of the.
- Variable annuities – Unlike fixed annuities, these are regulated by the SEC. They allow you to invest in portions of money markets.
- Equity-indexed annuities An equity index annuity in the United States is a type of tax-deferred annuity whose credited interest is linked to an equity index — typically the S&P 500 or international index. It guarantees a minimum interest rate if held to the end of the surrender term and protects against a loss of principal. An equity index annuity is a contract with – Lump sum payments are made to an insurance company.
Annuity due is useful for lease payment calculations 1
References
- ^ "Calculate Annuity Payment: Funding an Annuity". http://www.college-cram.com/study/finance/presentations/1128. Retrieved 2008-07-10.
- ^ Finite Mathematics, Eighth Edition, by Margaret L. Lial, Raymond N. Greenwell, and Nathan P. Ritchey. Published by Addison Wesley. ISBN 032122826X
- ^ http://www.AnnuityPayment.info
- ^ "Future Value of an Annuity Due". http://www.college-cram.com/study/finance/presentations/1129. Retrieved 2008-07-10.
- ^ ibid Lial.
See also
- Annuity (financial contracts) A life annuity is a financial contract in the form of an insurance product according to which a seller —typically a financial institution such as a life insurance company—makes a series of payments in the future to the buyer (annuitant) in exchange for the immediate payment of a lumpsum (single-payment annuity) or a series of regular payments (
- Perpetuity A perpetuity is an annuity that has no definite end, or a stream of cash payments that continues forever. There are few actual perpetuities in existence (the United Kingdom government has issued them in the past; these are known and still trade as consols). A number of types of investments are effectively perpetuities, such as real estate and
- Life annuity A life annuity is a financial contract in the form of an insurance product according to which a seller —typically a financial institution such as a life insurance company—makes a series of payments in the future to the buyer (annuitant) in exchange for the immediate payment of a lumpsum (single-payment annuity) or a series of regular payments (
- Fixed rate mortgage A fixed rate mortgage is a mortgage loan where the interest rate on the note remains the same through the term of the loan, as opposed to loans where the interest rate may adjust or "float." Other forms of mortgage loan include interest only mortgage, graduated payment mortgage, variable rate (including adjustable rate mortgages and
- Amortization calculator An amortization calculator is used to determine the periodic payment amount due on a loan , based on the amortization process
Categories: Finance theories
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FV = 0 i = 5 8 p a = 0 48333 per month PMT = Monthly installment is RM1056 16
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