Calculating Interest

Interest is increasingly important. It is the basis of savings, loans, investments, and mortgages. Learning about earning or losing capital makes a huge difference in how far your money goes. All interest is based off one simple formula:

I (interest) = P (principle) x R (rate) x T (time)

Simple interest (IPRT) is the standard equation applied to all loans. Interest is a dollar amount found by times principle and rate. Principle is the dollar amount lent or owed. Rate is the percentage paid or charged for the use of the money. Find the numerical value by dividing the rate by 100. Five percent divided by 100 equals 0.05. Time is the unit of time it takes to mature, pay off or compound: day, month, year or years.

For example, if you put $1,000 in the bank and the annual percentage rate is 4%, how much did you make that year?

I = 1,000 x 4% x 1 (4% is 4 divided by 100, so it becomes 0.04 for a calculator. It matures in one year so use 1.)

I = 1,000 x 0.04 = 40

The bank paid $40 to this person for keeping $1,000 in their savings account for one year.

If they kept $1,000 in the bank for 3 months, find the percentage of the year by dividing months in saving by months of the year.

I = 1,000 x 0.04 x (3/12) or I = 1,000 x 0.04 x 0.25 = $10

They made $10 in interest over three months. In business accounting a year equals: 360 days, 52 weeks or 12 months. Conservative lenders declare a year is 360 days, because they times 30 days by 12 months. Avoid confusion by asking about policies. Day traders and stock brokers often use a 365 day year to avoid confusion.

Compound Interest re-evaluates interest over a specified time:

I (interest) = (P (principle) x R (rate) x T (time)) + (In interest by the number of month)

Credit cards and annuities compound interest every month regardless of time. Since they follow a month-by-month basis they may claim a standard annual percentage rate; however, there is a slight difference.

If someone has an annuity plan based off on $1,000 that compounds monthly for 5% one year, how much did they make?



They made $51.17 on their investment. Compare this to simple interest.

I = 1,000 x 0.5 = $50.00.

The true annual percentage rate is 5.117%. However, if you were borrowing the money, you paid $1.17 more than 5% APR on the loan, because it was compounded. A year is divided by twelve to establish basic time units. Considering money only uses two decimal places, usually it is calculated to the third decimal and rounded to the nearest cent.

Credit cards are only paid when it has a balance owed. Principle compounds every month. Credit cards are convenient revolving credit lines, essentially loans. When a card is maxed minimum payments may only pay off new interest; therefore, a larger payment is necessary to pay off the loan.

Imagine buy something that cost $100 with 9.9% APR credit card to find how much money is going to the credit card companies. The minimum payment is $10.

We add an additional field for minimum payments.

Pn (principle by month) = (P (principle) + (In interest by the number of month) – M (minimum payment))



If you add the numbers in the In row, you will find the amount paid in interest is $4.83. By the tenth month and there was only $0.04 interest on the last payment. If it was a flat interest rate loan for ten months you would have paid $8.25 on $100 loan with a 9.9% annual interest rate. Therefore, by making monthly payments you saved $3.42 in interest.

Paying off credit cards has advantages. They become a problem when people buy more than their monthly payment and keep cards maxed. They are always paying the same, $0.83 in interest every month; instead of, paying it down.

Another disadvantage credit limits can be $1,000 with a minimum payment is $25. The interest on $1,000 is $8.25. Only $16.75 is paying off the principle. If it never paid off a lot of money is paying for the privilege of owning a credit card. Yet compound interest is preferred in investments and loans. People will say this isn't so; however, every payment decreases the principle. Think about that.

Sample exercise: Mike bought a game console for his son with a credit card. It has an annual percentage rate of 7.9%. The balance was paid off, because Mike only uses it in emergencies. The game console cost $282.20 with tax total. The minimum monthly payment is $25.

1. How much interest was paid on the first month?
2. How much interest was paid on the third month?
3. How much has been paid toward the principle on the third month?
4. How many months will it take to pay off the game console making a $75 payment each month when Mike made one payment of $75 shortly after buying the game console?
5. How much was paid in interest with the greater monthly payment?
6. How much did Mike save in interest during the same amount of time?

Answer Sheet


Review finances to discover if investments and debts are being handled responsibly. Ask a few questions to decide if changes are necessary or important. Is there a way to make larger payments? Can you eliminate credit cards usage on purchases without it affecting your personal or professional life? Will these changes help achieve long-term goals?

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