# Formulas To Solve Compound Interest Problems

## Compound Interest Formulas

### Definition

Compound interest is the interest calculated on the original principal and on the accumulated past interest of a deposit or loan. Compound interest is calculated based on the principal, interest rate (APR or annual percentage rate), and the time involved.

Amount = P (1+r/100)n

where, P = Principal

r = rate of interest

t = the number of years the amount is deposited or borrowed for.

n= the number of times that interest is compounded per unit ‘t’. ## Formulas for Compound Interest

### Formulas for Compound Interest (When Interest is Compound Annually)

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

### Formulas of Compound Interest (When Interest is Compound Half Yearly)

• Amount = P (1+r/2/100)2n
• Compound Interest = Total amount – Principal

### Compound Interest Formulas (When Interest is Compound Quarterly)

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

### Formulas of Compound Interest (When Interest is Compound Monthly)

• Amount = P (1+r/12/100)12n

### Compound Interest Formulas (When 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)

### Formulas of Compound Interest (When rates are different for different years)

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

### Formulas for Compound Interest (Present worth of Rs. x due n years)

• Present worth = x/(1+r/100)