## Loan with Variable Payments

This spreadsheet shows a loan with variable payments. Adding previously-accrued interest is important because the first three payments of $50 are less than the monthly interest charged.

As the “*Total Principal Balance*” increases in the first three rows, and so does the next month’s interest amount in the “*$ Interest /month*” column. That’s due to the additional interest applied to both the original principal of $10,000 and also to the “*Interest Balance*“.

Once the payment changes to $150.00, exceeding the monthly interest cost, the total balance begins to decrease. That reduces the next month’s interest cost.

In order to show the final payments, the monthly repayment ballooned to $1,000 or $5,195.72; but the same rules apply.

When you’re ready to make the last payment, ask your bank for the “*final payout amount*” to clear any remaining interest amount.

## Daily Interest or Savings

The same math rules apply for earning daily interest. The bank may set the daily rate as ‘*r/365*‘, where ‘r’ is the annual rate. They then calculate the compound interest on the daily balance; but usually all those daily amounts are reported as one interest cost or deposit on your monthly statement.

Interest calculations work the exactly the same for savings as for credit card balances, leases, loans or mortgages. There may be subtle differences, such as whether to apply the payment to the balance before *or* after calculating the interest cost.

## “Rule of 72” – How Long to Double Principal Due to Interest Alone

The difference between compound vs. simple interest is most obvious if you miss a credit card payment. Even if you don’t incur a penalty, there may be interest rates of 18% or more, applied to the “Rule of 72.”

The number of periods, ‘*n*‘, for your principal to double due to accrued interest added to your principal with additional interest calculated on the total, at rate ‘*r*‘ is approximately “*n=0.72/r*“, when ‘r’ is expressed as a number between zero and one. For example, if your savings earns 3%, the original principal doubles in about 24 years. (0.72/0.03 = 72/3 = 24 years or so.)

## Calculations: Other Applications

Many aspects of personal finances need to use compound interest calculations. Mortgage amortization is based on this type of interest, and loans often use compound interest calculations as well. In the US, credit cards charge interest on a compound basis, but in Canada, classic consumer credit cards must charge simple interest rather than compound.

We think of adding interest to principal in savings accounts as “growth.” Biologists may use the same type of calculation to model the growth of a plant, or the increasing number of bacteria in a colony. If a country’s population grows by a percentage annually, then it follows the same rules as well.

From credit cards to population growth – this is how you calculate compound interest.

## References

Annenberg Foundation. Savings and Credit. (2013). Accessed April 16, 2013.

Consumer Credit. *Credit Card Interest Calculator*. (2013). Accessed April 16, 2013.

Weisstein, Eric W. Compound Interest. From MathWorld–A Wolfram Web Resource. Accessed April 16, 2013.

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