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Being able to calculate interest, simple or compound, can help you be in control of your finances.
Let's say you need to buy a car that costs $10,000, but you do not have that money available. However, you can take out a loan because you can afford to pay a small amount each month until you pay off the car. If you know how to calculate the proposed interest, you can determine whether taking that loan is a good idea or not.
Same thing with compound interest. If you invest, how the interest is compounded can make a huge difference in the long run.
The benefits of knowing how to determine the interest or type of interest that best suits your financial needs is the reason I choose to try and learn and then try teaching this subject.

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You probably recognize this as the recursive form of exponential growth.  If not, we could go through the steps to build an explicit equation for the growth:

P0 = $1000

P¬1 = 1.0025P¬0 = 1.0025 (1000)

P¬2 = 1.0025P¬1 = 1.0025 (1.0025 (1000)) = 1.0025 2(1000)

P¬3 = 1.0025P¬2 = 1.0025 (1.00252(1000)) = 1.00253(1000)

P¬4 = 1.0025P¬3 = 1.0025 (1.00253(1000)) = 1.00254(1000)

Observing a pattern, we could conclude

Pm = (1.0025)m($1000)

Notice that the $1000 in the equation was P0, the starting amount.  We found 1.0025 by adding one to the growth rate divided by 12, since we were compounding 12 times per year.

Generalizing our result, we could write

In this formula:

m is the number of compounding periods (months in our example)

r is the annual  interest rate

k is the number of compounds per year.

While this formula works fine, it is more common to use a formula that involves the number of years, rather than the number of compounding periods.  If N is the number of years, then  m = N k.  Making this change gives us the standard formula for compound interest.

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With simple interest, we were assuming that we pocketed the interest when we received it.  In a standard bank account, any interest we earn is automatically added to our balance, and we earn interest on that interest in future years.  This reinvestment of interest is called compounding.

Simple Interest is great for loans as it does not compound interest -which would increase the amount you will ultimately pay back.

But when it comes to investments, you WANT a compounding interest.

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1. So if you borrow 100 from a friend and agree to pay it back with a 1 time 5% interest you will first have to calculate the amount of the interest and then add that to the principle-and this will be the amount you owe your friend in the end.

Principal = 100

Interest r =5% -that we have to convert to decimals.

to do that you divide 5 by 100 = 0.05

t =1 (since this is a one time interest)

r=100(0.05)(1) =5

A=the end amount (principal plus interest)

So the amount you would pay back is 100+5 =105

t is time –(days, months or years)depending on how the interest rate is given .

( A one-time rate, weekly, monthly, biyearly, quarterly ,yearly ) So time is expressed in the same period as the interest rate.

2. If you borrow 100 and agree to pay it back in a month with 5% weekly interest?

Then the 100 accumulates interest every week of that month-so 4 times.

P=100

t =4 (4 weeks in a month)

r0.05

100(0.05)(4)=20

A =100+20=120

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Simple one time interest  are usually great used for personal loans.

If you borrow money from a friend or a bank, you will use this simple Interest formula to calculate the interest amount that is added to the principle.

The principal is the initial amount borrowed. The interest is calculated based on this amount.

Calculating the simple one time interest is like the name suggests, simple by using the formula
I =Prt

P is the principal-the starting amount

r is the interest rate (written as a decimal)

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Discussing interest starts with the principal, or amount your account starts with.  This could be a starting investment, or the starting amount of a loan.  Interest, in its most simple form, is calculated as a percent of the principal.
For example, if you borrowed $100 from a friend and agree to repay it with 5% interest, then the amount of interest you would pay would just be 5% of 100:  $100(0.05) = $5.  The total amount you would repay would be $105, the original principal plus the interest.

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We have to work with money every day.  While balancing your checkbook or calculating your monthly expenditures on espresso requires only arithmetic, when we start saving, planning for retirement, or needing a loan, we need more mathematics.