Future Value Formula

Future Value Formula (Table of Contents)

Future Value Formula
FV Calculator
FV Template

Future Value Formula is a financial terminology used to compute the value of cash flow at a futuristic date as compared to original receipt. The objective is to understand the future value of a prospective investment and whether the returns yield sufficient returns to factor in the time value of money.

The formula for Future Value (FV) is:

Whereby,

C_{0 =}Cash flow at initial point (Present value)
r = Rate of return
n = number of periods

Example of Future Value Formula

Let us analyze some examples:

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 which has $20,000 paying an annual rate of 11% compounded on a quarterly basis. Since January 1, 2017, the terms of the agreement have been renewed and the compounded interest is attributed twice a month. Mrs. Smith wants to compute 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 interest 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 of Future Value Formula

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 factors 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 which 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 interest account will be the FV of every deposit.

Future Value Calculator

You can use the following Future Value Calculator

C₀
r
n
Future Value Formula =

Future Value Formula =

C₀ X (1 + r)ⁿ

0 * (1 + 0)⁰

Future Value Formula in Excel (with excel template)

Let us now do the same example above in Excel. This is very simple. You need to provide the two inputs of Present value, Rate of return and Number of periods. You can easily calculate Future Value in the template provided.

Example – 1