Math: compound interest, general case

Tutoring math 11 and 12, you encounter this formula.  The math tutor discusses the general case of compound interest.

I’ve discussed compound interest and exponential growth in numerous posts:here, here, and here. However, the focus has been on annual compounding, given by

A=P(1+r)^t

where A=accumulated amount, P=principal (the amount invested), r=annual interest rate in decimal form, and t=time in years.

Just to clarify: when interest is compounded, it becomes part of the principal. Then it, too, can start earning interest.

What about monthly compounding, which is applied to many charge accounts, etc? How is it calculated? The general formula is then used:

A=P(1+r/n)^(tn)

where n=number of compounding periods per year. (For monthly compounding, n=12.)

Example: Calculate the balance of an investment of $500 left in an account for five years, if the interest rate is 3.1% compounded monthly.

Solution:

Recall that 3.1% means 0.031.

A=500(1+0.031/12)^(5(12))=583.71

Now let’s repeat the example, but with weekly instead of monthly compounding:

A=500(1+0.031/52)^(5(52))=583.80

In today’s world of investing and credit, everyone needs to understand compound interest. I’ll bring more coverage of it in future posts:)

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.

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