Loan

reimbursement methods
Long-Term Loan Repayment Methods Money borrowed for long-term capital investments usually is repaid in a series of annual, semi-annual or monthly payments. Three different ways are used to calculate the amount of these payments 1. Equal total payments per time period (amortization); 2. Equal principal payments per time period; or 3. Equal payments over a specified time period with a balloon payment due at the end to repay the balance. When the equal total payment method is used, each payment includes the accrued interest on the unpaid balance, plus some principal. The amount applied toward the principal increases with each payment. The debt holder cashes out each year the same amount. The equal principal payment plan also provides for payment of accrued interest on the unpaid balance, plus an equal amount of the principal. The total payment declines over time. As the remaining principal balance declines, the amount of interest accrued also declines. The debt holder cashes out each year a different amount. These two plans are the most common methods used to compute loan payments on long-term investments. Table 1: Example of loan amortization: equal total payment plan. Loan amount ACE10 000, annual rate 12.8% annual payments Year 1 2 3 4 5 6 7 8 Total Annual payment ACE2 013.03 2 013.03 2 013.03 2 013.03 2 013.03 2 013.03 2 013.03 2 013.03 ACE16 104.24 Principal payment ACE 813.03 910.59 1 019.86 1 142.25 1 279.32 1 432.83 1 604.77 1 797.35 ACE10 000.00 Interest ACE1 200.00 1 102.44 993.17 870.78 733.71 580.20 408.26 215.68 ACE6 104.24 Unpaid balance 9 186.87 8 276.38 7 256.52 6 114.27 4 834.95 3 402.12 1 797.35 0 0 ACE10,000.00

Table 2: Example of loan amortization: equal principal plan. Loan amount ACE10 000, annual rate 12. 8% annual payments Year 1 2 3 4 5 6 7 8 Total Repayment Principles To calculate the payment amount, all terms of the loan must be known: interest rate, timing of payments (e.g., monthly, quarterly, annually), length of loan and amount of loan. Borrowers should understand how loans are amortized, how to calculate payments and remaining balances as of a particular date, and how to calculate the principal and interest portions of the next payment. This information is valuable for planning purposes before an investment is made, for tax management and planning purposes before the loan statement is received, and for preparation of financial statements. With calculators or computers, the calculations can be done easily and quickly. The use of printed tables is still common, but they are less flexible because of the limited number of interest rates and time periods for which the tables have been calculated. Regardless of whether the tables or a calculator is used, work through an example to help apply the concepts and formulas to a specific case. Lenders Use Different Methods Different lenders use different methods to calculate loan repayment schedules depending on their needs, borrowers' needs, the institution's interest rate policy (fixed or variable), the length of the loan, and the purpose of the borrowed money. Typically, home mortgage loans, automobile and truck loans, and Consumer installment loans are amortized using the equal total payment method. Annual payment ACE2 450.00 2 300.00 2 150.00 2 000.00 1 850.00 1 700.00 1 550.00 1 400.00 ACE15 400.00 Principal payment ACE1 250.00 1 250.00 1 250.00 1 250.00 1 250.00 1 250.00 1 250.00 1 250.00 ACE10,000.00 Interest ACE1 200.00 1 050.00 900.00 750.00 600.00 450.00 300.00 150.00 ACE5,400.00 Unpaid balance 8 750.00 7 500.00 6 250.00 5 000.00 3 750.00 2 500.00 1 250.00 0 0 ACE10,000.00

Lenders often try to accommodate the needs of their borrowers and let the borrower choose which loan payment method to use. A comparison of Tables 1 and 2 indicates advantages and disadvantages of each plan. The equal principal payment plan incurs less total interest over the life of the loan because the principal is repaid more rapidly. However, it requires higher annual payments in the earlier years when money to repay the loan is typically scarce. Furthermore, because the principal is repaid more rapidly, interest deductions for tax purposes are slightly lower. Principal payments are not tax deductible, and the choice of repayment plans has no effect on depreciation. The reason for the difference in amounts of interest due in any time period is simple: Interest is calculated and paid on the amount of money that has been loaned but not repaid. In other words, interest is almost always calculated as a percentage of the unpaid or remaining balance: I = i x R Where: I = interest payment i = interest rate R = unpaid balance. Amortization Tables An amortization table can determine the annual payment when the amount of money borrowed, the interest rate and the length of the loan are known. For example, an 8-year loan of ACE10,000 made at an annual rate of 12 percent would require a ACE2,013 payment each year. Using the Formulas Because of the infinite number of interest rate and time period combinations, it is easier to calculate payments with a calculator or computer than a table. This is especially true when fractional interest rates are charged and when the length of the loan is not standard. Variable interest rates and rates carried to two or three decimal places also make the use of printed tables difficult. Equal Total Payments For equal total payment loans, calculate the total amount of the periodic payment using the following formula: B = (i x A) / [1 - (1 + i)-N] Where: A = amount of loan, B = periodic total payment, and N = total number of periods in the loan.

 The principal portion due in period n is: Cn = B x (1 + i)-(1 + N - n) Where: C = principal portion due and n = period under consideration. The interest due in period n is: In = B - Cn. The remaining principal balance due after period n is: Rn = (In / i) - Cn. Equal Principal Payments For equal principal payment loans, the principal portion of the total payment is calculated as: C = A / N. The interest due in period n is: In = [A - C(n-1)] x i. The remaining principal balance due after period n is: Rn = (In / i) - C.