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.

Example 1:
 $2,080.80
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.


Example 2:
 $5,306.82
Explanation:

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






Become a member today (it’s Free)!


 Register with us

Are you a member? Sign in!


 Login to your account