Annuity Calculator

What is an annuity?

An annuity is a sequence of equal payments or disbursements. Individuals often find themselves in a situation where they have to pay or receive a certain amount of money at certain intervals (repayment of a loan or purchase of goods in installments, the partial return of investment amount funds at regular intervals). A life insurance contract is probably the most common and well-known type of business event involving a series of equal cash payments at equal intervals. Such a periodic savings process represents the accumulation of some amount of money through an annuity. The future amount of an annuity is the sum (future value) of all annuities that increase by the accrued interest. An annuity by definition requires:

1. periodic payments or receipts (annuities) are always of the same amount,
2. that the time interval between such annuities is always equal to and
3. calculation of an interest is once in each period.

It should note that you can make payments both at the beginning and at the end of the period. In order to distinguish between annuities in such situations. Annuities are can divide into:
1. regular annuities if payments are at the end of each period,
2. the annuities which payment is at the beginning of the period.

How to calculate annuity?

Calculating present value is a step toward estimating how much your annuity is worth — and if you’re receiving a fair bargain when you sell your payments. To comprehend and apply this method, you’ll need particular information, such as the discount rate given by a purchasing business. Given a fixed interest rate, the present value (PV) allows you to calculate the present value of equally spaced payments in the future. To determine the present value of an ordinary annuity, use the following annuity formula:

General annuity information

Annuities operate by turning a lump-sum premium into a fixed-income stream that a customer cannot outlive. To meet their everyday necessities, many retirees require more than Social Security and investment assets. Annuities can provide this income through an accumulation and annuitization process. In the case of instant annuities, lifelong payments guaranteed by the insurance company that begins within a month of purchase – no accumulation phase required.

Annuity arrangements shift to the insurance firm all of the risk of a falling market. This implies that you, as the annuity owner, are covered from market risk and longevity risk or the danger of outliving your money.

Quick pros and cons of annuities

Pros of annuities

• Lifetime income. Perhaps the most persuasive argument in favor of an annuity is that it typically offers income that cannot be outlived (though some only payout for a certain period of time).
• Deferred Distributions. Another attractive feature of annuities is the ability to make tax-deferred distributions. However, with annuities, you do not owe the government anything until you withdraw the cash.
• Guarantee rate. Variable annuities payout is based on how the market performs, whereas fixed annuities payout is based on a set rate of return over a set period of time.

Cons of annuities

• Fees are exorbitant. The main issue with annuities is their high cost when we compare it to mutual funds and CDs. Many are vend by agents, whose commission you pay in the form of a significant upfront sales price.
• Liquidity is scarce. Another source of concern is a lack of liquidity. Many annuities have a surrender charge that you must pay if you try to withdraw during the first few years of your contract.
• Increased tax rates. The tax-deferred status of your interest and investment profits is frequently cited as a key selling feature by issuers. When you do make withdrawals, however, any net returns you get are taxed as regular income. That may be far greater than the capital gains tax rate, depending on your tax status.
• Complexity. One of the most important investment principles is to never buy a product you don’t understand. Annuities are no different. Over the last several years, the insurance industry has erupted with a flood of new, often exotic variations on the annuity.

Fixed vs. Variable Annuities

Fixed annuities

A fixed annuity is a form of insurance contract that guarantees the customer a certain set interest rate on their contributions to the account. On the other hand, a variable annuity pays variable interest based on the success of an investment portfolio specified by the account’s owner.

Variable annuities

A variable annuity is a sort of annuity contract in which the value varies depending on the performance of an underlying portfolio of sub-accounts. Sub-accounts and mutual funds are essentially equivalent. However, sub-accounts lack ticker symbols that investors may readily enter into a fund tracker for research reasons. Variable annuities vary from fixed annuities in that they give a specified and guaranteed return.

Indexed annuities

An indexed annuity is a type of annuity contract that pays an interest rate based on the performance of a certain market index, such as the S&P 500. It differs from fixed annuities, which pay a fixed interest rate, and variable annuities, which base their interest rate on a portfolio of securities chosen by the annuity holder.

Immediate vs. deferred annuities

Immediate annuities

An immediate annuity is an agreement between an individual and an insurance company that pays the

owner a guaranteed income or annuity almost immediately. This is different from a deferred annuity, in which payments begin on a future date chosen by the annuity owner. An immediate annuity is also a lump-sum immediate annuity (SPIA), income pension, or simply an immediate annuity.

Deferred annuities

A deferred annuity could be a contract with an insurer that promises to pay the owner an everyday income or a payment at some future date. Investors often use deferred annuities to supplement their other retirement income, like Social Security. Deferred annuities differ from immediate annuities, which begin making payments straight away.

Surrendering an annuity

The surrender period is that the amount of your time an investor must wait until they withdraw funds from an annuity without facing a penalty. Surrender periods are often a few years long, and withdrawing money before the top of the surrender period may end up during a surrender charge, which is a deferred sales fee. Generally, but not always, the longer the surrender period, the higher the annuity’s other terms.

The difference between installments and an annuity

Both annuities and installments are monthly loan repayments, forming differently and significantly affecting the loan repayment amount.

Annuities are equal to monthly repayments. In which the ratio of the amount of principal and interest to the remaining principal changes with each repayment. The first annuity contains the lowest principal and the highest interest. Each subsequent month, the principal payment is more and more. The amount of interest decreases, while the total amount of annuities remains the same.

Installments are unequal monthly repayments in which a fixed amount is repaid in advance. Calculation of the amount of interest is on the remaining amount of principal. The first installment is the largest. Each subsequent installment is smaller than the previous one, while the last installment is the smallest. Although repayment in installments results in higher initial monthly payments. The user pays less total interest over a longer period of time. In future periods the monthly repayments in installments are relatively lower. Repayment in installments is fast and cheaper:

• the principal charge is quickly
• the total interest paid is less when repaying loans in installments than in annuities.

What are loans?

A loan is a property-legal relationship between a lender and a borrower. Regulation of that one the relationship is by a special loan agreement so that it defines:

a) the amount of the loan approved
b) interest rate
c) the manner in which the amount of interest will be calculated
d) loan repayment time
e) method of loan repayment

The borrower repays the loan to the lender with annuities. Annuities are periodic amounts consisting of repayment quotas and interest. Namely, at the end of the period, the obligation of the borrower is to repay the borrowed principal (loan), as well as the amount of accrued compound interest. An overview of the loan repayment is in the repayment table (plan). Which consists of columns that list: loan repayment period, annuities, interest, repayment quotas, and the rest of the debt. Loans can be non-purpose or cash, so-called. “Cash” loans and special purposes such as consumer, housing, or working capital. Only banks that have received a work permit can engage in lending operations, i.e., lending to legal entities and individuals.

Loan repayment model with equal annuities

We assume that the loan is repaid with a complex and decursive calculation of interest and equal annuities at the end of the period. Payment of the interest is throughout the repayment period the loan does not change. To determine the expression for the amount of equal annuities to which it is the loan of return, we notice an analogy between equal periodic payments at the end of the year and equal annuities and as between the present value of payments and approved loan. So the expression for the number of equal annuities at the end of the year will be analogous to the expression for the amount of periodic payments at the end of the year.

In practice, it is often easier to calculate the loan and provide an opportunity for the borrower to determine the amount of annuity that he assumes he will be able to repay, applying the loan repayment model to pre-agreed annuities.

What is interest?

Interest is the price of payment for the use of bank funds. If it is as a percentage, we are talking about the interest rate. The amount of the interest rate depends on the type of loan, the term for which the funds are shifting. The means of securing the collection of receivables, market conditions, competition, the inflation rate, and the country’s credit rating.

Nominal interest rate

Interest rate is a relative number – a percentage, which determines how many monetary units are per unit of credit and we use it to calculate regular interest on a given loan. It can be fixed or variable.

Conformal interest rate

Conformal interest rate is the rate at which the same amount of interest is obtained, regardless of whether the interest is calculated once at the end of the repayment period or more than once during the loan repayment. The annual conformal interest rate can be also a monthly interest rate by rooting the interest rate by the number of accounting periods. E.g. if the annual interest rate is 6%, we get the monthly by rooting 6% by the number of months 12. We get that the monthly is 0.487%.

Proportional interest rate

A proportional interest rate is a rate at which a different amount of interest is obtained depending on whether the interest calculation is once at the end of the repayment period or more than once during the loan repayment itself. Namely, suppose the interest is calculated more than once during the repayment period. In that case, a higher amount of total interest is obtained than if it was calculated only once at the end of the loan repayment period.

Suppose that the reduction of the proportional interest rate on an annual level to a monthly interest rate. In that case, it can obtain it by simply dividing the annual interest rate by the number of accounting periods. E.g., if the annual interest rate is 6%, the monthly come when we divide 6% by the number of months 12. We get that the monthly is 0.5%.

Effective interest rate

Unlike the nominal interest rate, the effective interest rate (EIR) represents the actual price of the loan. It allows you to more easily see and compare the conditions under which different banks offer the same loans.

In addition to the nominal interest rate, the effective interest rate includes fees and commissions paid by the client to the bank for the approval of the loan. In the case of loans granted with a deposit, the EIR also includes income based on the bank’s interest on that deposit. The effective interest rate also includes the cost of processing the application, the cost of issuing the loan, the annual fee for the loan administration fee, the fee for the unused portion of the framework loan, the amount of insurance premium, if insurance is a condition for using the loan, the costs of opening and maintaining accounts.

Condition for approving the loan, as well as other costs related to ancillary services that are a condition for using the loan and borne by the user (e.g., fixed fee for processing insurance claims, costs of issuing excerpts from the real estate register, costs of real estate appraisal and movables, costs of verification of the pledge statement, costs of registration of the pledge right – mortgage, costs of insight into the database on the indebtedness of the user, etc.).

Intercalary interest

Intercalary interest is the interest which calculation and charge are only from the moment you approve that loan until the moment you start repaying it, i.e., until the payment of the first installment. Depending on the business policy, the bank may accrue the accrued intercalary interest to the principal of the debt and collect it through an annuity/installment or at once – after the expiration of the loan. If the bank charges intercalary interest, you should check with the bank employees before concluding the contract when it would be best to pay off the loan so that the intercalary interest would be as low as possible.

Default interest

Default interest is an interest whose calculation and the charge is if the client has not settled the obligations in time in accordance with the provisions of the concluded contract.

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