Define the key elements of the simple interest loan. Principal (P) is the amount borrowed. Interest (I) is the total interest paid over a given time period. Rate (R) is the percent of the principal charged as interest each year, and time (T) is the time or period of the loan. The formulas used for simple interest rate loans define time in years.
Calculate the total amount to be paid back by first calculating the total interest (I) and adding it to the principal (P). For example, for a $5000 loan with an annual interest rate of 6% to be paid back over five years, use the simple interest formula I = PRT. In this case I = (5000) x (.06) x (5) or I = $1500. The total interest to be paid over the five year period is $1500.
Add the total interest to the principal to determine the total amount to be paid back. For example, a $5000 loan with a 6% interest rate and the time period of 5 years yields $1500 in total interest, which, added to the principal, yields $6500 to be repaid.
Define the payoff goal. For example, instead of the original five-year period, let the desired payoff period be three years.
Calculate the necessary payment to achieve the goal using the formula:
New Payment (NP) = (P + I) / T . Because payments on this loan are monthly, convert T from years to months in the formula by multiplying the years by 12 . For example, NP would be (5000 + 1500) / (3 x 12) or NP = 180.56. To pay off the loan two years ahead of schedule, a payment of $180.56 must be made monthly.
Define key elements of the loan. The Present value of the loan is (P). Interest (i) is the interest rate per interest period. The number of interest periods is (n). The uniform payment in a uniform series continuing for n periods is represented by (A).
Calculate the uniform payment (A) knowing the present value of the loan (P) and the interest rate (i) for a given time period (n) using the following equation: A = P [(i (1 + i)^n) / ((1 + i)^n) - 1)] . For example, if the original amount borrowed were $10,000 at a 7% annual interest rate for a period of five years, then A = 10,000[(.07 (1+ .07)^5) / ((1 + .07)^5) - 1)] or A = $2436.19 per year ($203.24 dollars per month).
Define the pay-off goal. For example, if the original loan period is five years and the desire is to pay off the loan two years early, the pay-off goal would be three years.
Calculate the new monthly payment to achieve the goal. Using the formula:
A = P [(i (1 + i)^n) / ((1 + i)^n) - 1)] P = 10,000, i = .07 and n becomes 3. Plugging in these values and solving for A yields A = 10,000 [(.07 (1 + .07)^3) / ((1 + .07)^3) - 1)] or A = $3810.52 per year ($317.54 per month) to pay off the loan in three years instead of five.