Compound Interest Formula

Compound interest calculation formula with examples.

Compound interest calculation formula

Future value calculation

The future amount after n years A_n is equal to the initial amount A₀ times one plus the annual interest rate r divided by the number of compounding periods in a year m raised to the power of m times n:

A_n is the amount after n years (future value).

A₀ is the initial amount (present value).

r is the nominal annual interest rate.

m is the number of compounding periods in one year.

n is the number of years.

Example #1:

Calculate the future value after 10 years present value of $3,000 with annual interest of 4%.

Solution:

A₀ = $3,000

r = 4% = 4/100 = 0.04

m = 1

n = 10

A₁₀ = $3,000·(1+0.04/1)^(1·10) = $4,440.73

Example #2:

Calculate the future value after 8 years present value of $40,000 with annual interest of 3% compounded monthly.

Solution:

A₀ = $40,000

r = 3% = 3/100 = 0.03

m = 12

n = 8

A₈ = $40,000·(1+0.03/12)^(12·8) = $50,834.74

Example #3:

Calculate the future value after 8 years present value of $50,000 with annual interest of 4% compounded monthly.

Solution:

A₀ = $50,000

r = 4% = 4/100 = 0.04

m = 12

n = 8

A₈ = $50,000·(1+0.04/12)^(12·8) = $68,819.76

Example #4:

Calculate the future value after 8 years present value of $70,000 with annual interest of 5% compounded monthly.

Solution:

A₀ = $70,000

r = 5% = 5/100 = 0.05

m = 12

n = 8

A₈ = $70,000·(1+0.05/12)^(12·8) = $104,340.98

 

 

Compound interest calculator ►

 

---

See also

• Compound interest calculator
• Effective interest rate calculation