So The amount after n years [A_{n]} is equal to the initial amount [A_{0]} 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).

A_{0} 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.

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

Solution:

*A*_{0} = $4,000

*r* = 4% = 4/100 = 0.04

*m* = 1

*n* = 10

*A*_{10} = $4,000·(1+0.04/1)^{(1·10)} = $5,920.98

Calculate the future value after 10 years present value of $6,000 with annual interest of 5%.

Solution:

*A*_{0} = $6,000

*r* = 5% = 5/100 = 0.05

*m* = 1

*n* = 10

*A*_{10} = $6,000·(1+0.05/1)^{(1·10)} = $9,773.37

Calculate the future value after 8 years present value of $25,000 with annual interest of 3% compounded monthly.

Solution:

*A*_{0} = $25,000

*r* = 3% = 3/100 = 0.03

*m* = 12

*n* = 8

*A*_{8} = $25,000·(1+0.03/12)^{(12·8)} = $31,771.71

Calculate the future value after 5 years present value of $55,000 with annual interest of 3% compounded monthly.

Solution:

*A*_{0} = $55,000

*r* = 3% = 3/100 = 0.03

*m* = 12

*n* = 5

*A*_{8} = $55,000·(1+0.03/12)^{(12·5)} = $63,888.92

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