# Interest Calculation

Description of the calculation of Interest with examples

## Calculation of Interest

The interest calculation is an extension of the percentage calculation. Interest is a percent value of one underlying or principal.

Base of the percentage calculation is the formula $$\displaystyle \frac{Z}{K}=\frac{P}{100}$$

• $$Z$$ = Interest
• $$K$$ = Principal
• $$P$$ = Interest rate

The formula can be changed for the value you are looking for

Interest     $$\displaystyle Z=\frac{K · P}{100}$$

Principal    $$\displaystyle K=\frac{Z · 100}{P}$$

Interest rate   $$\displaystyle P=\frac{Z · 100}{K}$$

## Calculate interest income

This example calculates the interest earned on investing $$3000$$ for one year at a fixed rate of $$3\%$$.

Given is the interest rate $$P = 3$$ and the capital = $$3000$$.

We are looking for the interest income $$Z$$.

The interest income is calculated according to the formula $$\displaystyle Z=\frac{K·P}{100}={3000·3}{100}=90$$

## Calculate interest rate

This example calculates the interest rate, which is required to receive $$150$$ interest in one year, from a capital of $$3000$$.

The capital $$K = 300$$ and the interest income $$Z = 150$$ are known.

We are looking for the interest rate $$P$$.

Calculated according to the formula $$\displaystyle P=\frac{Z·100}{K}=\frac{150·100}{3000}=5\%$$

## Calculate starting capital

What amount must be invested in order to receive an interest income of $$200$$ at a rate of $$5%$$? This question should be solved in this task.

he interest rate of $$P = 5\%$$ and the interest income $$Z = 200$$ are known

We are looking for starting capital $$K$$.

It is calculated according to the formula $$\displaystyle K=\frac{Z·100}{P}=\frac{200·100}{5}=4000$$

## Calculate interest income daily

For example, suppose you want to invest $$5000$$ for $$2$$ months at an annual interest rate of $$5\%$$. For this, the interest must be calculated on a daily basis. The formula for calculating the interest income is extended accordingly by the number of $$Tage = t$$. For each month, 30 days, so 360 days for 1 year are assume.

The capital $$K = 5000$$, the interest rate $$P = 5$$ and the number of days $$t = 60$$ are known

We are looking for interest income $$Z$$.

This is calculated $$\displaystyle Z=\frac{K·P}{100}·\frac{t}{360}=\frac{5000*5}{100}·\frac{60}{360}=41.67$$