Here we will have an in depth view of the way Future Value of Ordinary annuity and Annuity Due is calculated with mathematical formula and with MS Excel FV functions along with a handy calculator.
Stop wasting time with crappy templates - we bet, here you will find all you need!
| We are here to help! If you have any question or need a solution to a problem that relates to Future Value of lump sum, ordinary annuity and annuity due , we at ThinkAndDone.com will answer it. Just, fill in the details below providing us a contact email address so we can notify you when your answer or solution is ready | |
|
Your Name: |
Email: |
|
Problem/Question: |
|
Future Value Definition
If you have a sum of money sitting idle may be under your mattress or hidden below the soil in your garden, that sum of money loses it's value as time passes on. Thus the need to invest money in some venture that will increase its value, that investment may be buying stock of a company or for most ordinary folks like you and me it would mean an investment in a savings account at the local bank. Now if you deposited a sum of money in a Certificate of Deposit ( CD as they are commonly called ) then your money will earn interest and when the deposit matures some time in future you will have more money in your account than the sum you invested in. The process to ascertain this future sum of money is called determining the future value of a lump sum, or an annuity.
Future Value of a lump sum
As discussed earlier, say you deposited an amount of $1000 in bank account that paid an annual interest at the rate of 6%. How much money will you have if the term of the deposit is 5 years
Formula for Future Value of of a lump sum
FV = R x FVIF(i%,n)
where R is the initial amount
i is the interest rate
n is the number of years
FVIF is the interest factor which equals (1+i)n
Future Value Calculations for Lump Sum
Staying with the previous example, we would multiply the amount invested with the Future Value Interest Factor or FVIF to find the ending balance in your savings account
FV = $1000 x FVIF(6%,5years)
FVIF(6%,5years) = (1 + 0.06)5
FVIF(6%,5years) = (1.06)5
FV = $1000 x 1.3382255776
FV = $1338.23
What if we made period deposits or an annuity
The example we just discussed required finding future value of a lump sum but what if instead we had made a monthly deposit in to a bank account for a given number of years. Such periodic deposits makes it an annuity. The process to find the future value of an annuity varies depending on number of compounding periods and number of deposits in a year. We will illustrate the process with examples in just a moment.
Formula for Future Value of an annuity with constant cash flows?
Finding Future Value of an Ordinary Annuity
Say we were to deposit $1000 in a savings account each year for five years and the bank's interest rate was quoted as 8% annually. The periodic deposit of $1000 makes this an annuity, we will assume a deposit at the end of the month thus making it an ordinary annuity. Let us use the formula to find the ending balance in the account.
FV = R x [ (1+i)n - 1] / i
where R is the constant amount of the periodic deposit
i is the interest rate
and n is the number of years
FVA = $1000 x [ (1+0.08)5 - 1] / 0.08
FVA = $1000 x [ (1.08)5 - 1] / 0.08
FVA = $1000 x [ 1.4693280768 - 1] / 0.08
FVA = $1000 x 0.4693280768 / 0.08
FVA = $469.33 / 0.08
FVA = $469.33 / 0.08
FVA = $5866.63
Thus an investment in the savings account for five years yields an amount of $5866.63
Finding Future Value of an Annuity Due
In the last example we assumed the deposits were being made at the end of each year, which is very rare in case of bank accounts where usually we deposit the investment amounts at the beginning of the periods. When a series deposits are made at the start of the periods such an annuity is called an annuity due. So for the same amount of $1000 at 8% annual interest rate, how would we calculate the ending balance if it was an annuity due. The answer is simple, we multiply the ending sum with an extra interest factor of (1+i).
FVAD = $5866.63 x (1+0.08)
FVAD = $5866.63 x 1.08
FVAD = $6335.96
User submitted Future Value of Annuities Questions/Problems
Asked:
Bitanny Willis is looking to invest for retirment, which she hopes will be in 20 years. She is looking to invest in 22,500 today in the U.s treasury bonds that will earn interest at 6.25 precent annually. How much will she have at the end of the year?
Replied:
Hi Dawn
FV of $75,642
See the attached MS Excel WorkSheet for the equation for Common Stock Valuation and calculation of these results
Download MS Excel Worksheet for solutions to future value calculations
Asked:
Compound annunity- What is the accumulated some of each of the following streams of payments?
$500 a year for 10 years compounded annually at 6%.
$150 a year for 5 years compounded annually at 11%.
$35 a year for 8 years compounded annually at 7%.
$25 a year for 3 years compounded annually at 2%
Replied:
Hi Debbie
$500 a year for 10 years compounded annually at 6%.
Ordinary Annuity ( End of period deposits) : $6.590
Annuity Due: (Start of period deposits): $6,589
$150 a year for 5 years compounded annually at 11%.
Ordinary Annuity ( End of period deposits) : $934
Annuity Due: (Start of period deposits): $932
$35 a year for 8 years compounded annually at 7%.
Ordinary Annuity ( End of period deposits) : $359
Annuity Due: (Start of period deposits): $357
$25 a year for 3 years compounded annually at 2%
Ordinary Annuity ( End of period deposits) : $77
Annuity Due: (Start of period deposits): $75
See the attached MS Excel Worksheet for Excel formulas to find future value of ordinary annuity and annuity due
| A | B | C | D | E | |
|---|---|---|---|---|---|
| 1 | Future Value of Annuity | ||||
| 2 | R | 500 | 150 | 35 | 25 |
| 3 | N | 10 | 5 | 8 | 3 |
| 4 | I | 6% | 11% | 7% | 2% |
| 5 | FVA | =FV(B4,B3,-B2,0) | =FV(C4,C3,-C2,0) | =FV(D4,D3,-D2,0) | =FV(E4,E3,-E2,0) |
| 6 | FVAD | =FV(B4,B3,-B2,1) | =FV(C4,C3,-C2,1) | =FV(D4,D3,-D2,1) | =FV(E4,E3,-E2,1) |
| 7 | |||||