Calculators

Financial

Time Value of Money

FVIFA calculator. Calculate the future value interest factor of an annuity (FVIFA) and create a table of FVIFA values. Create a printable compound interest table for the future value of an ordinary annuity or future value of an annuity due for payments of $1.

Future Value of an Annuity

\[ \mathit{FV}=\dfrac{\mathit{PMT}}{i}[(1+i)^n-1](1+iT) \]

where i is the interest rate per period and n is the total number of periods with compounding occurring once per period.

Since the annuity is payments of $1, PMT = $1 and we have

\[ \mathit{FV}=\dfrac{\$1}{i}[(1+i)^n-1](1+iT) \]

T represents the type of annuity (similar to Excel formulas). If payments are at the end of the period it is an ordinary annuity and we set \(T = 0\). If payments are at the beginning of the period it is an annuity due and we set \(T = 1\).

Future Value of an Ordinary Annuity (FVOA)

If annuity type is ordinary, \(T = 0\) and the equation reduces to the formula for future value of an ordinary annuity

\[ \mathit{FVOA}=\dfrac{\$1}{i}[(1+i)^n-1] \]

Future Value of an Annuity Due (FVAD)

If annuity payments are due at the beginning of the period \(T = 1\) and the equation reduces to the formula for future value of an annuity due

\[ \mathit{FVAD}=\dfrac{\$1}{i}[(1+i)^n-1](1+i) \]

Where FVAD and FVOA are the future value, PMT is the recurring, identical, cash payment = $1, i is the interest rate in decimal form and n is the period number.

Example

Ordinary Annuity: You want to invest $5,000 at the end of every year into an account with an annual interest rate of 4%. What will be the value of your account at the end of 10, 15 and 20 years? These regular payments are an annuity.

1. Choose Ordinary Annuity
2. Create a table that includes \(i = 4\%\) and \(n = 10\), 15 and 20
   -- Start 10 columns at 1% with 1% increments
   -- Start 11 rows at 10 with increments of 1
3. Look up FVOA to find
   -- 4% @ 10 is 12.00611 and calculate $5,000 × 12.00611 = $60,030.55 at the end of 10 years
   -- 4% @ 15 is 20.02359 and calculate $5,000 × 20.02359 = $100,117.95 at the end of 15 years
   -- 4% @ 20 is 29.77808 and calculate $5,000 × 29.77808 = $148,890.40 at the end of 20 years
4. You can use these factors to easily compare other amounts. Let's say you might only invest $2,500 each year for 10 years
   -- 4% @ 10 is 12.00611 and calculate $2,500 × 12.00611 = $30,015.38 at the end of 10 years