Eight Standard >> Compound interest | Part-2

Half-yearly, quarterly and monthly compound interest

Illustration: Suppose we want to calculate the compound interest, when principal sum is Rs 5000, rate of interest is 10% per annual for 3 years compounded annually.

Ans:

\(A = P(1 + \frac{r}{n})^(nt)\)

Where: A = the final amount after time t (including the principal and compound interest) P = the principal amount (Rs 5000 in this case) r = the annual interest rate (10%, which is 0.10 as a decimal) n = the number of times interest is compounded per year (assuming annually, n = 1) t = the number of years (3 years in this case)

Now, let's plug in the values and calculate:

A =\( 5000(1 + \frac{0.10}{1})^(1*3)\)

A = \(5000(1 + 0.10)^3\)

A = \(5000(1.10)^3\)

(A = \(5000 * 1.331\)

A = 6655

So, after 3 years, the compound interest on Rs 5000 at a rate of 10% per annum, compounded annually, is (Rs 6655 - Rs 5000)= Rs 1655.

When the interest is compounded more frequently, such as half-yearly, quarterly, or monthly, the formula for compound interest changes slightly to take into account the compounding periods.

1. Interest Compounded Half-Yearly: The formula for compound interest when interest is compounded half-yearly is:

   A = \(P * (1 + \frac{r}{2})^(2*t)\)

   Where: A = the final amount after time t (including the principal and compound interest) P = the principal amount r = the annual interest rate (expressed as a decimal) t = the number of years

2. Interest Compounded Quarterly: The formula for compound interest when interest is compounded quarterly is:

   A = \(P * (1 + \frac{r}{4})^(4*t)\)

   Where: A = the final amount after time t (including the principal and compound interest) P = the principal amount r = the annual interest rate (expressed as a decimal) t = the number of years

3. Interest Compounded Monthly: The formula for compound interest when interest is compounded monthly is:

   A = \(P * (1 + \frac{r}{12})^(12*t)\)

   Where: A = the final amount after time t (including the principal and compound interest) P = the principal amount r = the annual interest rate (expressed as a decimal) t = the number of years

These formulas take into account the more frequent compounding periods, allowing for more precise calculations of compound interest when interest is applied more frequently throughout the year.