Learning Compound Interest

Compound interest is paid on the principal and also for the interest accumulated in the past years. Compound interest emerges when interest is added to the principal, so the interest that has been added also earns interest. This adding of interest with the principal is said to be compounding. Compounding can be done for a time like yearly, quarterly, monthly, daily etc.


Learning Compound Interest Formula:


Learning The basic formula for Compound Interest is:

FV = PV (1+r)n

PV is the present value

r is the annual rate of interest (percentage)

n is the number of years the amount is deposit or borrowed for.

FV = Future Value is the amount of money accumulate after n years, including interest.

Learning Frequent Compounding of Interest:

If interest is paid more frequently, Here are a few examples of the formula:

Annually = P × (1 + r) = (annual compounding)

Quarterly = P (1 + r/4)4 = (quarterly compounding)

Monthly = P (1 + r/12)12 = (monthly compounding)

Learning Find the Present Value when know a Future Value, the Interest Rate and number of Periods.

PV = FV / (1+r)n

Learning Find the Interest Rate when know the Present Value, Future Value and number of Periods.

r = ( FV / PV )1/n – 1

Learning Find the number of Periods when know the Present Value, Future Value and Interest Rate

n = ln(FV / PV) / ln(1 + r)

I like to share this mathematical induction with you all through my article.


Example of compound interest


Ex 1: I have $1000.00 to invest for 3 years at rate of 6% compound interest.

Sol:  Here p=$1000, n=3, r=5

A = 1000 (1 + 0.06)3 = $1191.02.

1000.00 is worth $1191.02

Ex 2:  How many years to turns 1000into10,000 at 5% interest?

Sol :    n = ln( 10000 / 1,000 ) / ln( 1 + 0.05 ) = ln(10)/ln(1.05) = 2.3026/0.04879 = 47.19

Ex 3 :  I have $2000.00 to invest for 3 years at rate of 7% compound interest.

Here p=$2000, n=3, r=7

A = 2000 (1 + 0.07)3 = $2450.09.

2000.00 is worth $2450.09.