The interest regime will be simple when the interest percentage is only on the principal amount. Interest generated in each period will not incur new interest. Principal or simply principal amount is the initial amount borrowed or invested before adding interest. Transforming into formula, we have:
J = P. i. no
|J = interest|
P = principal (capital)
i = interest rate
no = number of periods
Example: We have a debt of R $ 1,000.00 that must be paid with interest of 8% a.m. by the simple interest regime and we must pay it back in 2 months. The interest I will pay will be:
J = 1000 x 0.08 x 2 = 160
By adding interest to the principal amount, we have the amount.
Amount = Principal + Interest
Amount = Principal + (Principal x Interest Rate x Number of Periods)
M = P. (1 + (i.n))
Example: Calculate the amount resulting from applying $ 70,000 at the rate of 10.5% a.a. for 145 days.
M = P. (1 + (i.n))
M = 70000 1 + (10.5 / 100). (145/360) = $ 72,960.42
Note that we express the rate i and the period no in the same unit of time, ie years. Hence it has divided 145 days by 360, to get the equivalent value in years, since a business year has 360 days.
Simple Interest Exercises:
1) Calculate the simple interest from R $ 1,200.00 to 13% a.t. for 4 months and 15 days.
If the rate is 13% (ie 0.13) per quarter, let's divide it by 6 to find the rate every 15 days (since a quarter has 6 15-day periods):
0.13 / 6 = 0.02167
Thus, for 4 months and 15 days, the rate is 0.02167 x 9 = 0.195. Therefore:
J = 1200 x 0.195 = $ 234
2) Calculate the simple interest yielded for R $ 40,000.00, applied at the rate of 36% a.a., for 125 days.
We have: J = P.i.n
The rate of 36% a.a. equals 0.36 / 360 days = 0.001 a.d.
Now, as the rate and period refer to the same unit of time, ie days, we can calculate directly:
J = 40000.0.001.125 = $ 5,000.00
3) What capital applied to simple interest of 1.2% a.m. yields R $ 3,500.00 interest in 75 days?
We have immediately:
J = P.i.n
3500 = P. (1.2 / 100). (75/30)
Note that we express the rate i and the period no relative to the same unit of time, months. Soon,
3500 = P. 0.012. 2.5
3500 = P. 0.030;
P = 3500 / 0.030 = R $ 116,666.67
4) If an application rate is 150% per annum, how many months will it take to double an applied capital through simple capitalization?
Objective: M = 2.P
Data: i = 150/100 = 1.5
Formula: M = P (1 + i.n)
2P = P (1 + 1.5 n)
2 = 1 + 1.5 n
n = 2/3 year = 8 months