What is Annuity: Definition and 52 Discussions

An annuity is a series of payments made at equal intervals. Examples of annuities are regular deposits to a savings account, monthly home mortgage payments, monthly insurance payments and pension payments. Annuities can be classified by the frequency of payment dates. The payments (deposits) may be made weekly, monthly, quarterly, yearly, or at any other regular interval of time. Annuities may be calculated by mathematical functions known as "annuity functions".
An annuity which provides for payments for the remainder of a person's lifetime is a life annuity.

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  1. Eclair_de_XII

    Given price of an annuity and its level payments, find the interest rate

    A 30-year monthly-payment mortgage loan for 300,000 is offered at a nominal rate of 0.072 converted monthly. Thus the monthly effective interest rate is 0.006 and the calculated monthly payment is 2036.36. (Calculate the payment (PMT) on your calculator and leave it there for the moment.) When...
  2. S

    MHB Solve the $5000 Annuity Investment Today

    Dear All, Kindly help me by solving the following question, it gives me hard time to solve especially the word "commencing". Thank in advance. How much would need to be invested today at 6% per annum to provide an annuity of $5000 per ten years commencing in 5 years.
  3. I

    MHB Applying the annuity method - how?

    Hello, I was given following task: A food processing company has to make a decision whether or not to expand its production facilities. A feasibility study showed the following estimates: Initial cost outlay €800,000 Further outlay in 4 years €600,000 Residual value after 10 years €200,000...
  4. Monoxdifly

    MHB Ask About Annuity

    Mr. Budi borrows 2,000,000IDR which will be amortized with 10 annuities. The first annuity will be paid in 1 year with 10% per year interest. Make the installment plan! For the annuity I got A = M\times\frac1{\sum_{n=1}^p(1+i)^{-n}} = 2,000,000\times\frac1{\sum_{n=1}^{10}(1+0,1)^{-n}} =...
  5. N

    MHB Future Value of an Annuity

    In 6 years, Mattos Oil Refining Company wants to pay off a $50,000 debt in one lump sum amount. They must set up an account to accumulate the necessary funds to pay off their debt. If the payments are made every 6 months and the fund earns 9.6% compounded semiannually, what is the amount of each...
  6. I

    Calculate PV for Annuity Problem w/ 5.5% Discount Rate ($50K/yr Payments)

    Homework Statement The annually compounded discount rate is 5.5%. You are asked to calculate the present value of a 12-year annuity with payments of $50,000 per year. Calculate PV for each of the following cases. a. The annuity payments arrive at one-year intervals. The first payment arrives...
  7. I

    Annuity problem in Finance

    Homework Statement Mike Polanski is 30 years of age and his salary next year will be $40000. Mike forecasts that his salary will increase at a steady rate of 5% per annum until his retirement at age 60. If Mike saves 5% of his salary each year and invests these savings at an interest rate of...
  8. M

    MHB Present value of a perpetual annuity

    Hey! :o I want to determine the present value of a perpetual annuity, which will incur an interest payment of € 1 at the end of each year. A calculative interest rate $r$ is assumed. We are at the time $t = 0$, the first payout is in $t = 1$. Could you explain to me what an interest...
  9. W

    MHB Geometric annual annuity

    The geometric annual annuity runs for a period of 45 years which starts now. • The first payment at the end of the first year from now amounts to R2 000. • The growth rate of the annual payments equals 7% per year during the first 30 years (of the period of 45 years). • The growth rate of the...
  10. N

    Formula for annuity payments

    So, unless you've been living under a rock, you should know the jackpot for the powerball is at 1.5 billion dollars. I was looking up the distribution of annuity payments and the website said that the payments are not equally distributed. They are incremented by 5% each year. Like the nerd I...
  11. Y

    MHB Calculating x with an Annuity and Annual Rate of 44%”

    A car is purchased by 12 million by paying 48 monthly fee due to x each quarterly fee due and 400 000 each for four years . If a rate of 44% effective annual, determine the value of x . Answer from textbook is $353 137.09 Ussualy, in problems I've seen, annuity is separated, but here is...
  12. _N3WTON_

    Annunity Equation Derivation

    Homework Statement Solve the annuity problem: \frac{dS}{dt} = rS + d S(0) = S_0 Homework Equations Integrating factor method equation Future value of an annuity equation (this should be the final answer): S(t) = S_0e^{rt} + \frac{d}{r}(e^{rt} - 1) The Attempt at a Solution Ok, I am...
  13. U

    Interest Theory- Annuity Withdrawals

    Homework Statement Consider an investment of $5,000 at 6% convertible semiannually. How much can be withdrawn each half−year to use up the fund exactly at the end of 20 years? Homework Equations the present value annuity-immediate equation equation of value relating 5000 to the...
  14. J

    Annuity word problem

    Homework Statement A business is paying off a debt by paying an installment of $8000 at the end of each year. Interest is being charged at 5.5%. What is the outstanding debt if the business has just paid an installment and there remain 15 further installments of $8000 and a final repayment of...
  15. W

    Courses suggestions for a finance-wannabe?

    Hello all, I am an applied math/physics major who wishes to land on a finance-related jobs (including insurance) with a bachelor's degree. The coursework includes ODEs, PDEs, Calculus of Variations, Numerical Analysis, etc., with three faculty elective courses. Here is a list of courses that I...
  16. S

    Annuities Help please

    Hi guys I am trying to come up with an equation to solve for a break even point. Basically I have an initial outlay of cash with then a trail of income in the subsequent months. I need to know how often per year I need to receive this trail of income in order for the future discounted cash flows...
  17. P

    Compound investment - annuity

    Homework Statement Question is attached. Homework Equations sn = [a(1-r^n)]/(1-r) The Attempt at a Solution I know the more compounding periods there are, the better. The part that I'm stuck on is what values to put for r and n, since the rate that he is making payments is...
  18. P

    Annuity investment, find future value

    Homework Statement (attached) Homework Equations Sn = (a(1-r^n))/(1-r) The Attempt at a Solution This was my attempt, but I think I've done this wrong. I'm not really sure how to account for the fact that the payments are made at the end of the year. Unless that means I would act...
  19. micromass

    Schaum's Outline of Mathematical Handbook of Formulas and Tables

    Author: Seymour Lipschutz, Murray Spiegel, John Liu Title: Schaum's Outline of Mathematical Handbook of Formulas and Tables Amazon Link: https://www.amazon.com/dp/0071795375/?tag=pfamazon01-20 Prerequisities: None Table of Contents: Formulas Elementary Constants, Products, Formulas...
  20. P

    Probability: The Science of Uncertainty by Michael A. Bean

    I'm looking for a good and pedagogic book about introductory Probability and statistics. I'm trying to get into this subject by self study. I only have knowledge in basic calculus, a little about multivariable calculus and linear algebra. I studying physics but I don't how much I'll be needing...
  21. G

    Fuzzy investment advice

    http://thewitlessinvestor.wordpress.com/2012/03/27/you-won-the-lottery-lump-sum-or-annuity/ "If I invested my lump sum of $259 million today, and earned on average 10% from my investment, then is 26 years,... I will have around $3 Billion." Besides a grammar error: "then >is = IN< 26...
  22. N

    Finance formulas to compare the best value of a house

    Homework Statement House one is going for say 350.000 and House two is going for 250.000, both have the same bed and bath. Yet i want to add variables for instance house one has a decline in crime rate variable also a newly build mall. House two has new schools and crime is on the rise. So my...
  23. N

    Future Value of an annuity

    Homework Statement Mike needs $12.000 in 5 years. How much must he deposit at the end of each month for 5 years in an account paying 2.9% compounded monthly so that he will have $12.000 in 5 years? Homework Equations FV formula: S=R*((1+i)^n -1)/i I think that is the correct...
  24. N

    Finance problem recursive formula

    Homework Statement Daniel deposits $400 at the end of each month for 7 years in an account paying 1.6% compounded monthly. He then puts the total amount on deposit in another account paying 2.2% interest compounded semiannually for another 8 years. Find the final amount on the deposit after...
  25. N

    FINANCE annuity poblem, confused

    Eve deposited $8.000 in a 3-year certificate of deposit, which pays 2.2% compounded monthly. Find the account value at the end of the 3rd year and the amount of interest earned during the whole 3-year period. I think i use the payment to a sinking fund formula but i am not sure. possible...
  26. N

    At what point does math begin to describe the world in depth?

    I am taking Finite mathematics we learn things such as annuities and interest rates as well as matrices. Anyways i have taking math my entire life. And i do see the physical parts with things such as 1+1=2 but not in say y=5x+6 graphed out, or with isolating variables with functions like...
  27. Y

    Finding your annuity, Finding your reverse annuity

    ~TLDR at the bottom~ Homework Statement The Big question: Variables Account 1: P=250 R=.005 N=12 T=46 Variables Account 2: A1=155123.83 R=.0025 N=12 T=15 Homework Equations Annuity Formula(Given): A=P[(1+(r/n))nt)-1] ______________ (r/n)...
  28. Y

    Calculator issues?

    Homework Statement To save money you put $3000 at the end of each year in an annuity that pays 6.8% compounded annually. Use the formula for the value of an annuity. The Given Formula: A=P[(1+(r/n)nt)-1] ______________ (r/n) How much would be saved at the end of six years...
  29. M

    Financial Assignment involving annuities

    The Question is as follows; An individual age 30 is planning to start investing in a personal pension. Her aim is to have sufficient funds to provide a monthly pension of £1000 when she retires at the age of 65, payable for 30 years. She is able to make bi-annual contributions to the fund...
  30. J

    News What is the Asset Value of a College/University Degree?

    I'll try to put some numbers to this later. There has been a lot of discussion about the current cost of education and about changes in wealth for each age group over time. If we considered education as asset which yields about 19.5 thousand per year for about 40 years we can put a dollar value...
  31. J

    Electricity economics

    Hi, Here's my problem statement, followed by some calculations I consider and then from som questions I'll like to be answered. Homework Statement The household assumes that 60% of its consumption of electricity (both energy and power) is used for heating. Calculate the relative...
  32. P

    Math Modeling - Dynamical Systems -

    ***Ugh, I'm so sorry. I think I put this in the wrong thread. It probably should be in Calculus and Beyond... I tried to delete it but didn't see that option. So my professor gave us this problem to work on but no one could figure it out. I don't know where to even start and there's nothing at...
  33. K

    Weekly Annuity Calculation Method

    Homework Statement Consider a new Loan as below: InterestRate = 56.558% annual in arrear Amount = 1.000.000 Principal Payment Period = weekly (7 Days) Term = 25 weeks Homework Equations How to calculate the weekly installment amount? How's this "weekly principal payment" term has affect to the...
  34. M

    Theory of interest question.

    [b]1. 5. A twenty year annuity has end of month payments. The first year the payments are each $100. In subsequent years each payment increases by $10 over what it was the previous year. Find the present value of the annuity if i = 4% is the effective annual interest rate. Thank you
  35. O

    Financial Mathematics - Annuities

    http://www.intmath.com/Money-Math/annuity_6.gif [Broken] Above is the annuities formula (change the - to a + as i am not using it for loans) used to calculate the amount of money accumulated over a period of time with compounding interest, with a monthly input of $W. the first part is an...
  36. I

    Compound Interest / Annuities problem

    Suppose that you are negotiating your bonus with your boss. She offers you three options for your bonus: Option A: You get $5000 right now Option B: You get 8 monthly payments of $650 starting 1 month from now Option C: You get $5300, but you have to wait 8 months before you get it Using an...
  37. I

    Sum / Annuities question

    Find the final value of a plan in which payments of $800 are made every 6 months for 3 years, earning 10% interest compounded semi-annually. The first payment is made in 6 months. My Answer: R = 800, n = 6 , i = 5% A = R[(1-i)^n - 1] / i A = 800(1.05^6 - 1) / 0.05 A = $5441.53 So I...
  38. L

    Annuity Equation isolating n value HELP

    Annuity Equation "isolating n value" HELP! R =\frac{Pi(1+i)^n}{(1+i)^n-1} 1. I need to solve for n. n = number of years P = Investment R = Yearly Savings i = interest rate 3. My Attempt: R =\frac{Pi(1+i)^n}{(1+i)^n-1}\rightarrow -1 \cdot R = \frac{Pi(1+i)^n}{(1+i)^n} \cdot...
  39. C

    TVM Problem solving the end amount.

    [SOLVED] TVM Problem solving the end amount. Homework Statement 2. A spreadsheet software or TVM solver on a calculator can be used to determine the equal monthly payments that can be paid from an annuity for a set length of time. You can enter different payments until you find the one that...
  40. W

    Annuity differential equation

    I'm trying to figure out the solution to a differential equation that describes the accrued interest on an annuity - rather than a lump sum at the beginning, we're dealing with multiple and regular deposits. The prof implied that we would have to solve for the dif eq'n S' = k + rS where k is...
  41. T

    Any good sites for learning math?

    I starting in actuarial mathematics in September, so I would like to get ahead a bit and do some learning on my own. These are my obligatory courses: So if anyone knows a good place where I could get ahead and start learning any of these topics, please go ahead and post it.
  42. N

    How is Actuarial Mathematics?

    The course is a 400 level course but when I look at the description of it, I'm thinking it should be easy. Am I wrong? Course description: Topics include the economics of insurance, individual risk models for a short term, survival distributions and life tables, life insurance per year, life...
  43. G

    Which annuity formula to use?

    A father opened a savings account for his daughter on the day she was born, depositing $1000. Each year on her birthday he deposits another $1000, making the last deposit on her twenty-first birthday. If the account pays 9.5% interest compounded annually, how much is in the account at the end of...
  44. T

    Annuity compounded annually

    I am having trouble with the following problem: What will be the value of an annuity in today's dollars if $1000 is to be deposited for 18 years into an account paying 4.5% interest compounded annually? I used the following formula (I'm guessing I've figured something incorrectly) A=...
  45. S

    Annuities investment question

    i can't get these questions. how much is each payment for an investment of $32000... an interest rate of 12% per annum, compounded semi-annually, with payments every 6 months, starting in half a year. - i tried it but i can't seem to get the right answer... i think it might be the n...
  46. A

    Mortgage monthly payment?

    The current interest rate is 8.7%/a interest is compounded semi-annually and calculated monthly. The couple that is borrowing $90 000 for their new home wants to know how much it will cost them each month to pay off the loan. Assume they will make one payment per month. Calculate the monthly...
  47. A

    Fv=10 000 What do I do to find weekly payment general annuity

    Mary would like to save $10 000 at the end of 5 years for a future down payment on a car. How much should she deposit at the end of each week in a savings account that pays 12%/a compounded monthly, to meet her goal? This is a general ordinary annuity therefore before I make the line diagram...
  48. A

    Annuity confusion Help

    Annuity confusion Help please $100 is deposited at the beginning of every week for 5 years in an account that pays 14%/a compounded weekly this is a simple annuity due b)draw a line diagram to represent the annuity what is the line diagram going to show present value or future value...
  49. I

    Annuities: Determining the Interest Rate

    Annuities: Determining the Interest Rate (help needed!) David has $2000 to invest in an annuity. What interest rate must be obtain in order to receive payments of $500 at the end of each year for the next 5 years?
  50. M

    News How Galveston, TX opted out of Social Security

    How Galveston, TX opted out of Social Security... http://www.tppf.org/government/perspect/holbrook.html [Broken] :smile: