# Tag Archives | compound

## Rule of 72

The rule of 72 is an approximation tool used to determine the amount of time it will take for money to double on the earnings of compound interest.

## Rule of 72 Explained

The rule of 72 is essentially an estimation for determining the amount of years or the doubling time of an investment. Do this by taking the interest available on the investment. Then divide it by 72. This type of investing is usually fairly accurate, it is more accurate with lower interest rates than it is for higher ones. It is normally used solely for compound interest situations and is not a very good indicator if the investment earns a simple interest at the end of the investment term. This rule is most useful if an investor cannot perform an exponential function and simply needs to do simple math for an estimate of an investment.

## Rule of 72 Formula

Use the following rule of 72 formula:

Doubling Time (# years) = 72/Interest Rate

## Example

What is the doubling time for an investment with a compound interest rate of 8%? A person using the rule of 72 equation would find the doubling time equal to 9 years. Calculate it by dividing 8 by 72. By performing this, the investor can tell that it will take approximately 9 years to double the principal. It is fairly accurate as the exponential function yields an actual doubling time of 9.006 years. 0

# Interest Expense Formula

Interest expense calculations involve 4 parts: Principal, Rate, Time, and Compounding.

Use the following formula to calculate simple interest expense (which excludes compounding):

Interest Expense = Principal X Rate X Time

To calculate the compound interest rate, use the following formula:

Principal X (1+ (R / N))(N X T)

Where:
R = Interest rate
N = Number of times interest is compounded in a year
T = Time in years

Interest Expense Calculation Principal = \$50,000 Interest Rate = 7% Time = 3 years

\$50,000 X .07 X 3 = \$10,500 in interest expense

## Interest Expense Journal Entry

When recording an interest expense journal entry, the interest expense account is debited and the cash account or the interest payable account is credited. This represents money coming out of the cash or interest payable account and going into the interest expense account.

If you have already recorded the interest payment as a liability, then it may show up on the balance sheet as interest payable. If it has not already been recorded as a liability on the balance sheet, then the amount used to pay for the interest expense will come out of the cash account or the prepaid interest account on the balance sheet. Make this journal entry when the interest expense is recognized.

### Journal Entry Example

Depending on the circumstances, the journal entry may look like one of the following:

```                                 Debit                Credit

Interest Expense                  \$1,000
Cash                                          \$1,000

Interest Expense                  \$1,000
Interest Payable                              \$1,000

Interest Expense                  \$1,000
Prepaid Interest                              \$1,000```

Interest Expense Example

Dwayne has started a company which rents party equipment. The equipment in which he rents are too expensive to buy straight up. Dwayne is considering financing some equipment, mainly the additional trucks he needs to move supplies, so that he could provide a high level of service. Dwayne wonders what his interest expenses would be. He looks on the web to find an “interest expense calculator”. Dwayne calculates these results:

Principal: \$50,000 Interest: 7% Time: 3 years Compounding: None

So:

\$50,000 X .07 X 3 = \$10,500 in interest expense

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## Effective Rate of Interest Calculation See Also:
What is Compound Interest
When is Interest Rate Not an Important in Selecting a Loan?
Nominal Interest Rate
Interest Rate Swaps
Fixed Interest Rate vs Floating Interest Rate

# Effective Rate of Interest Calculation

An effective rate of interest calculation is the actual cost of a loan. It is the total amount of interest paid on a loan, expressed as a percentage of the principal. Effective annual interest rates incorporate the effects of compounding.

## Effective Annual Rate Formula

Effective annual interest rates are calculated in the two following ways:

1. Effective Rate = Total Interest Paid / Principal Amount

2. Effective Rate = (1 + i / n)n – 1

(Where i is the nominal rate and n is the number of compounding periods per year.)

For example, using the first formula, if the starting principal amount is \$1,000 and the total interest paid over the course of the year is \$104.70, then the effective interest rate is 10.47%. So, look at the following calculation:

.1047 = 104.7 / 1000

Using the second formula, if the starting principal amount is \$1,000, the nominal annual interest rate is 10%, and the rate is compounded monthly, then the effective annual rate is 10.47%. Look at the following calculation:

.1047 = (1 + .10/12)12 – 1

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# Bank Charge Definition

Bank charge, defined as the fees associated maintaining a bank account, exist in the personal as well as business world. These charges come from two factors. First, regular account maintenance is perhaps the most common. Additionally, fees due to violations of agreements, bank charges for insufficient funds as an example, also occur.

## Bank Charge Explanation

Bank charge, explained as the common fees from banking, form the most common costs of maintaining accounts. For normal accounts, banks may charge fees such as monthly or yearly account maintenance fees, transaction fees, transfer fees, and more. For violations, bank charges for businesses may be caused by undergoing the minimum balance, insufficient funds, minimum savings amounts, and more.

The reason bank charges exist is so that banks can maintain reliable customers. These fees are levied to discourage bad policies which, if compounded, result in issues with the bank itself. Bank charge refunds may be given but are uncommon due to corporate policies.

Bank charges can be the result of other situations with a bank. It is important to understand the agreement made with a bank upon creation of a business or personal account. Additionally, account holders will want to educate themselves on bank policies regularly to be abreast of new policies, changes, and other amendments.

## Bank Charge Example

Jonah is the manager of a branch of a major bank. As the manager, he has a variety of responsibilities from managing employees, monitoring performance, creating and maintaining branch policies, upholding corporate policies for both workers and account holders, and processing major transactions. Jonah has much to do when he shows up to work each day.

Jonah must now decide on how to uphold policies with an important business account holder. In this situation, the account owner was charged for insufficient funds. The problem with this is that the company deposited a check to cover this, however the check came at the end of the work week. The bank does now process checks on the weekend. Though a bank charges complaint letter has been sent to the corporate office Jonah must make the final decision.

Jonah meets with the company account manager. This man, one of the controllers of company finances, makes multiple cases to attempt to gain the funds lost from this accident. Despite this, Jonah can not give the company a break. Corporate policies dictate that Jonah must maintain his stance.

Jonah is able to compromise by waving the monthly account fees. This is able to soften the blow of the mistake. Jonah wants to make sure to keep happy customers and maintain good word-of-mouth. Overall, he is successful at this. Jonah leaves work happy that he was able to provide some value to his customers. 0

# Annual Interest Rate Definition

The Annual percentage rate (APR) of a loan is the yearly interest rate expressed as a simple percentage. A bank or lender quotes the rate or APR. The annual percent rate does not incorporate the effects of compounding.

The federal Truth in Lending Act requires all consumer loan agreements to show the APR in large bold type. This is to make it easier for consumers to compare borrowing costs from different lenders. However, the annual percentage rate may not be the most accurate representation of the cost of the loan.

If interest on the loan compounds more than once per year, then the annual percent rate will be less than the actual interest rate on the loan, which is called the effective interest rate or the effective annual rate (EAR). In order to see the true cost of the loan, it is necessary to convert the annual percentage rate into the effective annual rate.

## Annual Interest Rate Equation

If the lender offers a loan at 1% per month and it compounds monthly, then the annual percentage rate (APR) on that loan would be quoted as 12%. The annual percentage rate does not include the effects of compounding, so it is less than what the borrower would actually pay. Below is the annual interest equation for APR.

12% = 1% per month x 12 months

APR = Rate per period x Periods per year

## Effective Annual Rate Formula

If the lender offers a loan at 1% per month, and the loan compounds monthly, the effective annual rate (EAR) on that loan would be 12.68%. The effective annual rate does include the effects of compounding, so it is higher than the APR. The EAR reflects what the borrower actually pays in interest on the loan. Below is the effective annual rate formula.

12.68% = (1 + 1%)12

EAR = ( 1 + (APR/N)N ) – 1

(Where N = the number of compounding periods per year.)

## Convert APR to Monthly Interest

To convert annual rate to monthly rate, when using APR, simply divide the annual percent rate by 12.

Monthly Rate = APR / 12 Strategic CFO Lab Member Extra

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