FORMULABANK

To determine the amount initially deposited in the account when you know how many periods the money has been held and the interest rate.

The formula is as follows:

$F_0=\frac{F_n}{{(1+r)}^n}$

• _Fn = Final capital / final value
• _F0 = Initial capital / initial value
• r = Interest rate / growth rate in % per period
• n = Number of periods

Example:

Claire currently has 1500 DKK. The money has grown by 10% per month (the periods in this example). How much money did she have 5 months (periods) ago?

Calculation Example:

Using the formula:

$K_0=\frac{1500}{{(1+\mathrm{10\backslash \%})}^5}\approx 931.382$

Alternatively:

Substituting known values into the "basic growth formula" and solving in WordMat:

$1500=K_0\cdot (1+\mathrm{10\backslash \%})$⁵

The equation is solved for K₀ using the CAS tool WordMat:

$K_0=931.382$

This means that Claire had approximately 931.38 DKK 5 months ago.