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Time Value of Money

Welcome to Our Site

Samdom For Peace I greet you this day,
You may use these calculators to check your answers. You are encouraged to solve the questions first, before checking your answers. Please do not use a comma.
I wrote the codes for these calculators using Javascript, a client-side scripting language.
In addition, I used the JavaScript library, Formula.js for some calculations.
Please use the latest Internet browsers. The calculators should work.
You may need to refresh your browser after each calculation to clear all results of a calculation.
Comments, ideas, areas of improvement, questions, and constructive criticisms are welcome. You may contact me. Thank you for visiting!!!

Samuel Dominic Chukwuemeka (SamDom For Peace) B.Eng., A.A.T, M.Ed., M.S





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Symbols and Meanings


NOTE: Unless instructed otherwise;
For all financial calculations, do not round until the final answer.
Do not round intermediate calculations. If it is too long, write it to at least $5$ decimal places ($5$ or more decimal places).
Round your final answer to $2$ decimal places.
Make sure you include your unit.

Formulas


It is very important you use these formulas with the meaning of the symbols
In the case of the same formula written in several different ways, use whatever formula is convenient for you.

Basic Formulas

$ (1.)\:\: i = \dfrac{APY}{m} \\[7ex] (2.)\:\: n = mt \\[5ex] (3.)\:\: For\:\:Compounding\:\:Interest:\:\: effective\:\:interest\:\:rate = APY \\[5ex] (4.)\:\: For\:\:Continuous\:\:Compounding\:\:Interest:\:\: effective\:\:interest\:\:rate = e^{APY} - 1 \\[5ex] $

Values of $m$
If Compounded: $m = $
Annually $1$ ($1$ time per year)
Also means every twelve months
Semiannually $2$ ($2$ times per year)
Also means every six months
Quarterly $4$ ($4$ times per year)
Also means every three months
Monthly $12$ ($12$ times per year)
Also means every month
Weekly $52$ ($52$ times per year)
Daily (Ordinary/Banker's Rule) $360$ ($360$ times per year)
Daily (Exact) $365$ ($365$ times per year)


Single Cash Flow

$ (1.)\:\: PV = \dfrac{FV}{\left(1 + i\right)^n} \\[7ex] (2.)\:\: PV = FV * \left(1 + i\right)^{-n} = FV * single\:\:payment\:\:present\:\:worth\:\:factor \\[5ex] (3.)\:\: PV = \dfrac{FV}{\left(1 + \dfrac{APY}{m}\right)^{mt}} \\[10ex] (4.)\:\: FV = PV * (1 + i)^{n} = PV * single\:\:payment\:\:compound\:\:amount\:\:factor \\[5ex] (5.)\:\: FV = PV * \left(1 + \dfrac{APY}{m}\right)^{mt} \\[7ex] (6.)\:\: APY = m\left[\left(\dfrac{FV}{PV}\right)^{\dfrac{1}{mt}} - 1\right] \\[10ex] (7.)\:\: APY = m\left(10^{\dfrac{\log\left(\dfrac{FV}{PV}\right)}{mt}} - 1\right) \\[10ex] (8.)\:\: APY = m\left[\left(\dfrac{FV}{PV}\right)^{\dfrac{1}{n}} - 1\right] \\[10ex] (9.)\:\: APY = m\left(10^{\dfrac{\log\left(\dfrac{FV}{PV}\right)}{n}} - 1\right) \\[10ex] (10.)\:\: t = \dfrac{\log\left(\dfrac{FV}{PV}\right)}{m\log\left(1 + \dfrac{APY}{m}\right)} \\[10ex] (11.)\:\: t = \dfrac{\log\left(\dfrac{FV}{PV}\right)}{m\log(1 + i)} \\[7ex] $

Uniform Cash Flows (Ordinary Annuities)

$ (1.)\:\: PV = UCF * \left[\dfrac{(1 + i)^n - 1}{i(1 + i)^n}\right] \\[7ex] (2.)\:\: PV = UCF * uniform\:\:series\:\:present\:\:worth\:\:factor \\[5ex] (3.)\:\: PV = UCF * \left[\dfrac{\left(1 + \dfrac{APY}{m}\right)^{mt} - 1}{i\left(1 + \dfrac{APY}{m}\right)^{mt}}\right] \\[10ex] (4.)\:\: PV = m * UCF * \left[\dfrac{1 - \left(1 + \dfrac{APY}{m}\right)^{-mt}}{APY}\right] \\[10ex] (5.)\:\: FV = UCF * \left[\dfrac{(1 + i)^n - 1}{i}\right] \\[7ex] (6.)\:\: FV = UCF * uniform\:\:series\:\:compound\:\:amount\:\:factor \\[5ex] (7.)\:\: FV = UCF * \left[\dfrac{\left(1 + \dfrac{APY}{m}\right)^n - 1}{\dfrac{APY}{m}}\right] \\[10ex] (8.)\:\: FV = m * UCF * \left[\dfrac{\left(1 + \dfrac{APY}{m}\right)^{mt} - 1}{APY}\right] \\[10ex] (9.)\:\:Sinking\:\:Fund:\:\: UCF = FV * \dfrac{i}{(1 + i)^n - 1} \\[7ex] (10.)\:\:Sinking\:\:Fund:\:\: UCF = FV * sinking\:\:fund\:\:factor \\[5ex] (11.)\:\:Sinking\:\:Fund:\:\: UCF = \dfrac{FV * APY}{m * \left[(1 + i)^{n} - 1\right]} \\[10ex] (12.)\:\:Sinking\:\:Fund:\:\: UCF = \dfrac{FV * APY}{m * \left[\left(1 + \dfrac{APY}{m}\right)^{mt} - 1\right]} \\[10ex] (13.)\:\:Amortization:\:\: UCF = PV * \dfrac{i(1 + i)^n}{(1 + i)^n - 1} \\[7ex] (14.)\:\:Amortization:\:\: UCF = PV * capital\:\:recovery\:\:factor \\[5ex] (15.)\:\:Amortization:\:\: UCF = \dfrac{PV * APY}{m * \left[1 - (1 + i)^{-n}\right]} \\[7ex] (16.)\:\:Amortization:\:\: UCF = \dfrac{PV * APY}{m * \left[1 - \left(1 + \dfrac{APY}{m}\right)^{-mt}\right]} \\[10ex] (17.)\:\: t = \dfrac{\log\left[\dfrac{FV * APY}{m * UCF} + 1\right]}{m * \log\left(1 + \dfrac{APY}{m}\right)} \\[10ex] (18.)\:\: t = -\dfrac{\log\left[1 - \dfrac{PV * APY}{m * UCF}\right]}{m * \log\left(1 + \dfrac{APY}{m}\right)} \\[10ex] $

NOTE: Unless instructed otherwise;
For all financial calculations, do not round until the final answer.
Do not round intermediate calculations. If it is too long, write it to at least $5$ decimal places ($5$ or more decimal places).
Round your final answer to $2$ decimal places.
Make sure you include your unit.





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Single Cash Flows


Compound Interest
  • Given: present value, number of compounding periods per year, interest rate, time
    To Find: future value, interest

  • $\%$ per


    Compounded per



  • Given: future value, number of compounding periods per year, interest rate, time
    To Find: present value, interest

  • $\%$ per


    Compounded per



  • Given: present value, number of compounding periods per year, future value, time
    To Find: interest, interest rate per year

  • Compounded per




  • Given: present value, number of compounding periods per year, interest rate, future value
    To Find: interest, time

  • $\%$ per


    Compounded per







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Uniform Cash Flows


Ordinary Annuity
  • Given: periodic uniform cash flows, interest rate, time
    To Find: future value, interest
  • per


    $\%$ per



  • Given: periodic uniform cash flows, interest rate, time
    To Find: present value, interest
  • per


    $\%$ per



Sinking Fund
  • Given: future value, interest rate, time
    To Find: periodic uniform cash flows, interest
  • obtained by


    Compounding the uniform cash flow per


    $\%$ per



Amortization
  • Given: present value, interest rate, time
    To Find: periodic uniform cash flows, interest
  • obtained by


    Compounding the uniform cash flow per


    $\%$ per



  • Given: periodic uniform cash flows, interest rate, future value
    To Find: time, interest
  • per


    $\%$ per



  • Given: periodic uniform cash flows, interest rate, present value
    To Find: time, interest
  • per


    $\%$ per



  • Given: periodic uniform cash flows, time, future value
    To Find: interest rate, interest
  • per




  • Given: periodic uniform cash flows, time, present value
    To Find: interest rate, interest
  • per








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Deferred Ordinary Annuity
  • Given: periodic uniform cash flows, interest rate, time
    To Find: future value of deferred ordinary annuity, interest
  • per


    $\%$ per




  • Given: periodic uniform cash flows, interest rate, time
    To Find: present value of deferred ordinary annuity, interest
  • per


    $\%$ per








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