Formula to Calculate FV
Future Value (FV) Formula is a financial terminology used to calculate the value of cash flow at a futuristic date as compared to the original receipt. The objective of this FV equation is to determine the future value of a prospective investment and whether the returns yield sufficient returns to factor in the time value of moneyFactor In The Time Value Of MoneyThe formula to calculate time value of money (TVM) either discounts the future value of money to present value or compounds the present value of money to future value. FV = PV * (1 + i/n )n*t or PV = FV / (1 + i/n )n*tread more.
The formula for Future Value (FV) is:
Whereby,
- C0 = Cash flow at the initial point (Present value)
- r = Rate of return
- n = number of periods
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For eg:
Source: Future Value Formula (wallstreetmojo.com)
Example
If Mrs. Smith has $9,000 in her bank account and she earns an annual interest of 4.5%. With the help of the future formula, her account after 15 years will be:
- FV = 9,000 * (1 + 0.045) ^ 15
- FV = 9,000 * (1.045) ^ 15
- FV = 9,000 * 1.935
- FV = $17,417.54
We can consider another example for better understanding:
Mrs. Smith has another account that has $20,000 paying an annual rate of 11% compounded on a quarterly basisCompounded On A Quarterly BasisThe compounding quarterly formula depicts the total interest an investor can earn on investment or financial product if the interest is payable quarterly and reinvested in the scheme. It considers the principal amount, quarterly compounded rate of interest and the number of periods for computation.read more. Since January 1, 2017, the terms of the agreement have been renewed, and the compounded interest is attributed twice a month. Does Mrs. Smith want to calculate the total value of the account on December 31, 2017?
We firstly need to arrive at the opening balance as on January 1, 2017:
- PV (Jan’16 – Dec’16) = $20,000
- Compounding period (n) = 4
- Annual interest rate (r) = 11% which converts to quarterly interest of 2.75 % [11% / 4]
- FV = 20,000 * (1 + 0.0275) ^ 4
- FV = 20,000 * (1.0275) ^ 4
- FV = $22,292.43 (This is the opening balance as of January 1, 2017)
Thus, now for calculating Future value as of 31st December, 2017, the Present value if $22,292.43.
Compounding period (n) now is 2*12 = 24 since the compound interestCompound InterestCompound Interest is the interest earned from the initial Principal & the previously accumulated Interest amount. This is also known as “Interest on Interest” & it is always higher than the Simple Interest. read more is now twice a month.
Annual interest (r) = 11% which converts monthly interest rate = 11%/12 = 0.0092 [this will further be split twice a month thus, 0.92/2 = 0.0046%]
- Thus, FV = PV (1 + r) ^ n
- FV = 22,292.43 * (1 + 0.0046) ^ 24
- FV = 22,292.43 * (1.00046) ^ 24
- FV = 22,292.43 * 1.116
- FV = $24,888 [Value of the account as on December 31, 2017]
Use and Relevance
- The primary benefit of FV is to determine whether an investment opportunity will garner sufficient yield in the future.
- The concept is applicable to Personal and Corporate decisions.
- The objective is to have an understanding of how economic factorsEconomic FactorsEconomic factors are external, environmental factors that influence business performance, such as interest rates, inflation, unemployment, and economic growth, among others.read more can have an impact on the earnings such as Inflation, Standard of living, operating expenses/recurring expenses (separate analysis is required to be done).
- It shows the stream of payments that are expected to receive over a period of time, e.g., a 10-year investment can show how much returns can be earned every year.
- In certain circumstances, the formula is also used as an input to other formulas. For e.g., annuity in the form of recurring deposits in an interesting account will be the FV of every deposit.
Future Value Calculator
You can use the following Future Value Calculator
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Future Value Formula Video
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This has been a guide to Future Value Formula. Here we learn how to calculate future value (FV) using its formula along with practical examples, a calculator, and a downloadable excel template. You may also have a look at these articles below to learn more about Corporate Finance
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