Future Value Formula

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 Time Value of Money (TVM) principle states that money received in the present is of higher worth than money received in the future because money received now can be invested and used to generate cash flows to the enterprise in the future in the form of interest or from future investment appreciation and reinvestment.read more.

The formula for Future Value (FV) is:

FV=C₀ * (1+r)ⁿ

Whereby,

C_{0 =}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 31^st 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 charged on the sum of the principal amount and the total interest amassed on it so far. It plays a crucial role in generating higher rewards from an investment.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.