# Formulas for Simple Interest And Compound Interest

## Formulas To Find Averages In Aptitude

When interest is calculated on the principal, or original amount.Then, it is known as Simple Interest.When interest is calculated on the principal amount and also on the interest of previous time periods. Then, it is known as Compound Interest  .Compound Interest also known as Interest on interest.

### Definition of Simple Interest

• The interest calculated on the amount initially invested or loaned. It is a method for calculating the interest earned or paid on a certain balance in a specific period.
• Simple interest is a quick and easy method of calculating the interest  on a sum of Amount. It is determined by multiplying the daily interest rate by the principal amount and the number of days .

### Definition Of Compound Interest

• Compound interest is the addition of interest to the principal sum of a loan or deposit. Compound interest is calculated based on the principal, interest rate, and the time period involved.
• It is the addition of interest to the sum of Amount  or Principal Amount i.e.  interest on interest. It is the result of reinvesting interest.So that interest in the next period is then earned on the principal amount and previously accumulated interest.

### Formula for Compound Interest

• Interest Compounded Annually
• Amount = $\mathbf{P\left ( 1+\frac{R}{100n} \right )^{nT}}$
• Compound Interest = Total amount – Principal
• Rate of interest (R)(in %) = $n[(\frac{A}{P})^{\frac{1}{nT}} – 1]$

### Interest Compounded Half-Yearly

• When interest is compounded Half yearly Then, we must consider n=2, Hence, Formula for  Amount = $\mathbf{P\left ( 1+\frac{R}{100\times 2} \right )^{2T}}$
• Compound Interest = Total amount – Principal
• Rate of interest (R) (in %)= $2(P^{\frac{1}{2T}} – 1)$

### Interest Compounded Quarterly

• We have to consider n=4. So, Amount =  $\mathbf{P\left ( 1+\frac{R}{100\times 4} \right )^{4T}}$
• Compound Interest = Total amount – Principal
• Rate of interest (R) (in %)= $4(P^{\frac{1}{4T}} – 1)$

### Interest is Compound Monthly

• When the interest is compounded montly then, n=12. So, formula for  Amount = $\mathbf{P\left ( 1+\frac{R}{100\times 12} \right )^{12T}}$

### Interest is Compounded Annually but Time is in Fraction, say 2(3/2) years

• When the Interest is Compounded Annually but Time is in Fraction. Then, the formula  Amount = P (1+r/100)2 * (1+(3/2)r/100)$\mathbf{(1+ \frac{r}{100})^{2}}$$\mathbf{(1+ \frac{\frac{3r}{2}}{100})}$

### CI when Rates are Different for Different Years

• When rates are different for different years . Then, Amount = P $(1+ \frac{r_{1}}{100})(1+ \frac{r_{2}}{100})(1+ \frac{r_{3}}{100})$

### Formula for Simple Interest

• Simple Interest

SI = $\mathbf{\frac{P * R * T}{100}}$

Where,

P = money borrowed or lent out for a certain period

r = rate of interest

t = time period for which the amount is lent

Principal = $\frac{100 × SI}{R × T }$

Rate = $\frac{100 × SI}{P × T }$

Time = $\frac{100 × SI}{R × P }$

### Total Amount of Money

• Amount = Principal + Interest
• A = P + I

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