# Formula for Compound Interest Calculation

Computation for compound interest is complicated as compared to simple interest. There are a lot of things to be considered and observed properly to avoid miscalculations of the future amount. Below is the formula to get the future amount for compound interest.

## Future Amount = Principal X  (1+ text(Rate per Period))^text(Number of Periods)

Sometimes the future amount has non-terminating decimals simply because of the division used to calculate the rate of interest per period.If this happens so, round off the digits at least to the nearest hundredths.

##### Explanation:

An amount of $2,000 is invested at a rate of 2% compounded yearly. How much will be the amount after 2 years? Answer:$2,080.80

Explanation:

Principal is $2,000. Rate of interest is 2% compounded yearly. Number of years is 2. Determining the rate of interest per period; Rate per Period  = text(Nominal Rate)/text(Periods per Year) Note: There is 1 period for every year because it is yearly. Rate per Period  = (2%)/( 1) = 2% Determining the number of periods; Number of Periods = Periods per Year x Number of Years Number of Periods = 1 x 2 Number of Periods = 2 Using the formula for solving the future amount; Future Amount = Principal x (1 + text(Rate per Period))^ text(Number of Periods) Future Amount =$2,000 x (1 + 0.02)^2

Future Amount = $2,000 x (1.02)^2 Future Amount =$2,000 x 1.0404

Future Amount = $2080.80 Therefore, the amount becomes$2,080.80 after 2 years.

Principal is $5,000. Rate of interest is 6% compounded quarterly. Number of years is 1. Determining the rate of interest per period; ## Rate per Period  = text(Nominal Rate)/text(Periods per Year) Note: There are 4 quarters in a year. ## Rate per Period  = (6%)/( 4) = (6%)/( 4) = 1.5% Determining the number of periods; Number of Periods = Periods per Year x Number of Years Number of Periods = 4 x 1 Number of Periods = 4 Using the formula for solving the future amount; Future Amount = Principal x (1 + text(Rate per Period))^ text(Number of Periods) Future Amount =$5,000 x (1 + 0.015)4

Future Amount = $5,000 x (1.015)2 Future Amount =$5,000 x 1.016

Future Amount = \$5,306.82

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