# Formulas For Simple Interest And Compound Interest Problems

## 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.

## 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. ## Formula for Compound Interest

### Interest Compounded Annually

• Amount = P (1+r/100)t
• Compound Interest = Total amount – Principal
• Rate of interest (R) = [(A/P)1/ t − 1] %

### Interest Compounded Half-Yearly

• Amount = P (1+r/2/100)2t
• Compound Interest = Total amount – Principal
• Rate of interest (R) = 2*[P1/t − 1] %

### Interest Compounded Quarterly

• Amount = P (1+r/4/100)4t
• Compound Interest = Total amount – Principal

### Interest is Compound Monthly

• Amount = P (1+r/12/100)12t

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

• Amount = P (1+r/100)2 * (1+(3/2)r/100)

### CI when Rates are Different for Different Years

• Amount = P (1+r1/100) (1+r2/100) (1+r3/100)

## Formula for Simple Interest

### Simple Interest

SI = 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 = 100* SI/ R * T
• Rate = 100* SI/ P * T
• Time = 100* SI/ R * P

### Total Amount of Money

Amount = Principal + Interest

A = P + I

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Simple and Compound interest
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