Retirement annuity plan

The Accumulation Phase of a retirement plan is a period of an individual's life in which they are working and are able to save money for retirement. The accumulation phase begins when an individual starts to save money for retirement and ends when they start to receive distributions.

When individuals decide to buy an annuity they agree to pay a lump upfront or to make regular deposits to the insurance institution. The money individuals pay to the insurance companies is then reinvested into the market. Money grows until the day when an individual decides to retire.[2]

The payback phase starts as soon as distributions are paid to the insured individuals. There are different ways how insurance organizations can distribute payments. Payments could be distributed for a predetermined period of time (e. g. 15 years) annually, semi-annually, etc.; as well as in the form of a life annuity or a single payment. Payments could be paid immediately after the retirement of an individual or after some period of time.

Individuals that enter into a fixed annuity have the opportunity to decide ahead of time how much they will receive when the distribution phase begins. A Fixed annuity enables fixing the rate of return for a predefined number of distribution periods or for life. Generally, fixed annuities are conservative insurance products as the rate of return is approximately equal to the rate of return that certificate of deposit (CD) would offer.[3][4]

Variable annuities operate in other ways. The final value of distributions that would accumulate from investments an individual had made during the accumulation phase is directly dependent on the performance of the investment options that would be chosen by the client. Individuals typically use mutual funds that invest in market instruments, bonds, and (or) stocks.

Payments on it begin after a certain period of time. This period can vary widely (from one year to several decades). A deferred annuity is often used to organize pension payments - the accumulation phase in it can last until a certain age of the annuitant.

An immediate retirement annuity is an annuity that is purchased in a single lump sum, and payments on it begin immediately (30 days to 12 months), after the entry into force of the contract (there is no accumulation phase). An immediate annuity is good for turning a large amount of money into a source of permanent income (some kind of pension). It is not widely used as there is no accumulation phase, but it is suitable for rich people that would like to retire and purchase a passive source of income.[5][6]

A purchase of a retirement annuity could help individuals to shift the financial risks of retirement to the insurance company. With fixed retirement annuities insured retirees will receive the fixed amounts of money no matter how the financial markets are moving.[7]

Another great benefit of an annuity is that it is not taxed until the payout phase. The annuitant is responsible to pay the taxes on the distribution, but generally on the income earned on top of the original investment.[8]

This insurance product is very flexible and there are many types of annuity plans that can suit almost anyone recording to their own preferences.[9]

One of the main downsides of retirement annuity is costs. Comparing to other financial instruments such as investing in mutual funds and certificates of deposit. As retirement annuities are often sold by intermediaries the cost of commission is shifted to a buyer.[10]

Very often individuals who closed deferred retirement annuities will have to pay a surrender fee if they unexpectedly will withdraw funds during the early years of the contract. However, most annuities allow for emergency purposes a penalty-free withdrawal, which varies from 10% to 15% of the account.

Calculate a lump sum payment that an individual should pay to the insurance organization, in order to in 20 years receive monthly distributions in the amount of $500 for 5 years, assuming a constant annual rate of return 12%.

Calculation of a monthly nominal ROR...r

${\displaystyle r={j \over m}={0.12 \over 12}=0.01=1\%}$; where j...constant annual ROR, m...number of months

${\displaystyle _{240|}a_{{\overline {60}}|1\%}=500\cdot v^{240}\cdot a_{{\overline {60}}|1\%}=500\cdot {\left({\frac {1}{1.01}}\right)^{240}}\cdot \left({\frac {1-{\left({\frac {1}{1.01}}\right)}^{60}}{0.01}}\right)=2063.46\$}$; where ${\displaystyle _{240|}a_{{\overline {60}}|1\%}}$...lump sum payment, ${\displaystyle v={\frac {1}{1+r}}}$...discount factor,

${\displaystyle a_{{\overline {n}}|r}={\frac {1-v^{n}}{r}}}$...the present value of $1 annuity immediate.

Calculate a lump sum payment that and individual should pay to insurance organisation, in order to for the next 20 years receive annual variable distributions. The first distribution of $30.000 in the first year is decreasing each next year by $1.000.  Assume constant annual rate of return 5%.

${\displaystyle {\begin{aligned}PV&={30000}\cdot v+{29000}\cdot v^{2}+\cdots +{11000}\cdot v^{20}\\&={31000}(v+v^{2}+\cdots +v^{20})-{1000}\cdot (v+2v^{2}+\cdots +20v^{20})\\&={31000}\cdot a_{{\overline {20}}|r}-1000\cdot (ra)_{{\overline {20}}|r}\\&={31000}\cdot {\frac {1-v^{20}}{r}}-{1000}\cdot {\frac {(1+r)\cdot a_{{\overline {20}}|r}-20\cdot v^{20}}{r}}\\&={31000}\cdot {\frac {1-{\left({\frac {1}{1.05}}\right)}^{20}}{0.05}}-1000\cdot {\frac {(1+r)\cdot a_{{\overline {20}}|r}-20\cdot {\left({\frac {1}{1.05}}\right)}^{20}}{r}}\\&={31000}\cdot {12.462210}-1000{\frac {1.05\cdot {12.462210}-20{\left({\frac {1}{1.05}}\right)}^{20}}{0.05}}\\&=31000\cdot 12.462210+1000\cdot 110.950616\\&=386328.51+110950.616\\&=497279.126\end{aligned}}}$

where ${\displaystyle 30000\cdot v=31000\cdot v-1000\cdot v=(310000-1000)\cdot v=30000\cdot v}$ and ${\displaystyle 29000\cdot v^{2}=31000\cdot v^{2}-1000\cdot 2v^{2}=(310000-1000\cdot 2)\cdot v^{2}=29000\cdot v^{2}}$ etc.