.Compounding

Question

Math Question:  If the interest rate is 3% compounded semiannually, this is represented in the compound formula as .03/2.  If the interest rate is 7%, how would that percent be represented in the compound interest formula if it was compounded quarterly.  How would thisproblem be worked?

Answer 1

7% would be 0.07/4 per quarter period. The growth rate per interest period is 1+r making the total growth applied to a starting amount for n interest periods (1+r)ⁿ. If time y is measured in years then n=2y for semiannual compound interest and n=4y for quarterly compound interest.

Reduced to figures, for semiannual or quarterly periods the growth factor per accounting period is 1.015 or 1.0175. In one year this is 1.015²=1.030225 or 1.0175⁴=1.071859 approx. You can see that for one year’s growth these values are close to 3% or 7%, depending on the given annual interest rate. But as time goes on the difference between simple and compound interest becomes more noticeable until it’s far higher for compound interest.