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.
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;
Note: There are 4 quarters in a year.
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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