FORMULABANK

Final Capital (Fn)

Economics and Growth

Final capital (Kn) is used to determine the account balance after n periods with interest accrued per period.

The formula is as follows:

$F$_n=F₀⋅(1 + r)ⁿ

• F_n = Final capital / final value
• F₀ = Initial capital / initial value
• r = Interest rate / growth rate in % per period
• n = Number of periods

Example:

Roger deposits 1000 in an account with an annual interest rate of 3%. How much money will be in the account after 5 years (which are 5 periods in this case)?

Calculation Example:

Using the formula:

$F$_n=1000⋅(1 + 0.03)⁵ ≈ 1159.274

Alternatively:

$F$_n=1000⋅(1 + 0.03)⁵

The equation is solved for K_n using the CAS tool 

$F$_n=1159.274