Compound Interest
Compound Interest: \( F = P(1+i)^t \)
The formula \( F = P(1+i)^t \) calculates the future value \( F \) of an investment or loan, where:
- \( P \) is the principal (initial amount);
- \( i \) is the interest rate per period (in decimal form);
- \( t \) is the number of periods.
For example, if an investment of \( P = 1000 \) euros is made at an annual interest rate of 5% for 3 years, then:
\[ F = 1000(1+0.05)^3 = 1157.63 \]
Hence, the investment will grow to 1157.63 euros after 3 years.
Interest Calculation: \( I = F - P \)
When an investment of \( P \) results in a future value of \( F \), the accumulated interest \( I \) is given by:
\[ I = F - P \]
For instance, if an initial investment of \( P = 1000 \) euros results in a future value of \( F = 1157.63 \) euros, then the interest accumulated is:
\[ I = 1157.63 - 1000 = 157.63 \]
Thus, the interest accrued over 3 years is 157.63 euros.
Depreciation: \( F = P(1-i)^t \)
The depreciation formula \( F = P(1-i)^t \) computes the future value \( F \) of an asset that loses value over time, where:
- \( P \) is the initial value;
- \( i \) is the rate of depreciation per period (in decimal form);
- \( t \) is the number of periods.
For example, if an asset purchased for \( P = 20000 \) euros depreciates at an annual rate of 10% for 5 years, then:
\[ F = 20000(1-0.10)^5 = 11809.80 \]
Therefore, the asset’s value will depreciate to 11809.80 euros after 5 years.
Calculator and Graph
Compound Interest - Future Value Calculator and Graph
\( F = P(1+i)^t \)
About the Formula
The compound interest formula calculates the future value (\(F\)) of an investment given:
- P: the principal (initial amount in euros)
- i: the interest rate per period (expressed as a decimal, e.g. 0.05 for 5%)
- t: the number of time periods (in years)
By substituting these values into the formula, the calculator computes the future value of your investment.
Future Value Challenge
Compound Interest
Can you calculate the interest earned?
