How To Use Amortized Loan - Normal Interest

The most common method of repaying an interest-bearing loan is by amortization. In this method, a series of periodic payments is made. The indebtedness at any time is called the outstanding balance or outstanding principal. It is just the discounted value of all unmade payments.

Each sequential payment pays the interest on the unpaid balance and also repays a part of the outstanding principal. Over the term of the loan, as the outstanding principal decreases, the interest portion of each payment decreases and the principal portion increases. This shifting distribution is shown in an amortization schedule. Amortized loan is calculated according to this schedule. Payments are set up using the formula given below.

RULE OF 78's

The difference between the above method and Rule of 78's is that, in the Rule of 78's, the interest portion of each payment is not determined by the unpaid balance, but rather by a calculation which is called Rule of 78's. This may result in a different distribution shift than described above. As well, if a loan is paid off early, with Rule of 78's computing, a borrower does not receive as much of an interest refund as in other forms of borrowing.

Please see How to Use the Rule of 78 Interest for details and formulas used in this type of calculation.

Amortized Loan Information

In the Interest Detail form, the Operator enters:

• Annual Interest Rate - as a percent, e.g. 15. This is the Annual rate of interest. When Period is more frequent than Annual, Interest rates are calculated for the Period using the formula -- R/n
• Period - pick a Period from the list. This is a frequency of interest conversion (compounding) and a frequency of payment. Collect! uses this information to determine how often to compound Interest. It also states how often a debtor is scheduled to make a payment.
• Rate Basis - 360, 364 or 365 days, or Ordinary - 12 months. This is the length of the year.
• Calculate Interest From Date - the date you want calculation to begin.
• Term - this is the Total Number of Payments. It is NOT in the formula below. If the debtor is paying monthly for four years, that means 12 payments for 4 years so Term = 48.
• First Payment Date - the date you want the first payment to be due.

These are the basic values that Collect! needs to set up the pre-amortization schedule and display results of calculations. There are additional options you can choose. Press F1 in the Interest Detail form for information on the field you are wondering about.

Payment Amount

Collect! uses the following formula to calculate Payment amount. The Operator enters the information listed above and Collect! performs the necessary calculations.

Full formula:

$\mathrm{Payment}=\frac{\left(\right(\frac{\mathrm{AmountBorrowed}\left(\frac{\mathrm{AnnualInterestRate}}{100}\right)}{\mathrm{PaymentsPerYear}}\left)\right(1+\frac{\left(\frac{\mathrm{AnnualInterestRate}}{100}\right)}{\mathrm{PaymentsPerYear}}{)}^{\mathrm{NumberOfPayments}})}{\left(\right(1+\frac{\left(\frac{\mathrm{AnnualInterestRate}}{100}\right)}{\mathrm{PaymentsPerYear}}{)}^{\mathrm{NumberOfPayments}}-1)}$

The Above formula appear complicated due to the fact that we are dividing the Annual Interest Rate in Collect! by 100 to get a decimal. By doing that first, the formula appears more simplified:

$\mathrm{Payment}=\frac{\left(\frac{\mathrm{AmountBorrowed}\mathrm{AnnualInterestRate}}{\mathrm{PaymentsPerYear}}\right)(1+\frac{\mathrm{AnnualInterestRate}}{\mathrm{PaymentsPerYear}}{)}^{\mathrm{NumberOfPayments}}}{\left(\right(1+\frac{\mathrm{AnnualInterestRate}}{\mathrm{PaymentsPerYear}}{)}^{\mathrm{NumberOfPayments}}-1)}$

Example:

$2000 borrowed at 5% for 2 years with Monthly payments.

Plugged into the formula:

$\mathrm{Payment}=\frac{\left(\frac{2000*0.05}{12}\right)(1+\frac{0.05}{12}{)}^{24}}{\left(\right(1+\frac{0.05}{12}{)}^{24}-1)}$

Approximately, this results in 8.3333 x 1.10494 divided by .10494 which gives a monthly payment of $87.74.

Total Plan Payments

Total Plan Payments amount is calculated as follows:

$\mathrm{TotalPlanPayments}=\mathrm{PaymentAmount}*\mathrm{NumberOfPayments}$

In our example, this is 87.74 x 24 = $2105.76

If the Set Terms Manually switch is ON, the Payment Amount is supplied and Payment Amount formula is not used.

Total Interest

To calculate the Total Interest, the following is used:

$\mathrm{TotalInterest}=\mathrm{TotalPlanPayments}-\mathrm{AmountBorrowed}$

In our example, this is 2105.76 - 2000.00 = $105.76

Time In Years

Calculations take into consideration the Rate Basis set in the Interest Detail. This Rate Basis is used in every single interest calculation. It can be set to Ordinary, 360, 364 or 365 days.