You simple interest they are corrections made to an applied or due amount. Interest is calculated from a pre-established percentage and takes into account the period of application or debt.
An applied amount is called capital, the correction percentage is called interest rate. The total amount received or due at the end of the period is called amount.
In many everyday situations, we face financial problems. Therefore, it is very important to understand this content well.
So, take advantage of the commented exercises, solved and contest questions, to exercise on the simple interest.
Commented Exercises
1) João invested R$20,000 for 3 months in a simple interest application at a rate of 6% per month. What is the amount received by João at the end of this application?
Solution
We can solve this problem by calculating how much interest John will receive each month applied. That is, let's find out how much is 6% of 20 000.
Remembering that percentage is a ratio whose denominator is equal to 100, we have:
So, to know how much interest we will receive per month, just multiply the amount applied by the correction rate.
Interest received per month = 20 000. 0,06 = 1 200
For 3 months we have:
1 200. 3 = 3 600
In this way, the amount received at the end of 3 months will be the amount applied plus the interest received in the 3 months:
Amount received (amount) = 20 000 + 3 600 = 23 600
We could also have solved the problem using the formula:
M = C (1 + i. t)
M = 20,000 (1 + 0.06. 3) = 20 000. 1,18 = 23 600
See too: how to calculate percentage?
2) In a store, a TV set is sold with the following conditions:
What is the interest rate charged on this loan?
Solution
To find out the interest rate, we must first know the amount that interest will be applied. This amount is the outstanding balance at the time of purchase, which is calculated by decreasing the amount related to the payment in cash of the amount paid:
C = 1750 - 950 = 800
After one month, this amount becomes an amount of R$ 950.00, which is the value of the 2nd installment. Using the amount formula, we have:
Thus, the interest rate charged by the store for this payment option is 18.75% per month.
3) A capital is applied, at simple interest, at the rate of 4% per month. How long, at least, should it be applied in order to be able to redeem triple the amount applied?
Solution
To find the time, let's replace the amount with 3C as we want the value to be tripled. Thus, substituting in the amount formula, we have:
In this way, to triple in value, the capital must remain invested by 50 months.
Solved Exercises
1) A person applied a simple interest principal for 1 year and a half. Adjusted at a rate of 5% per month, it generated an amount of R$35,530.00 at the end of the period. Determine the capital invested in this situation.
t = 1 year and a half = 18 months
j = 5% = 0.05
M = 35 530
C = ?
M = C (1 + it)
35 530 = C (1 + 0.05. 18)
35 530 = 1,9. Ç
C = 35 530 / 1.9
C = 18 7 00
Thus, the capital applied was BRL 18,700.00
2) The water bill for a condominium must be paid by the fifth business day of each month. For payments after maturity, interest is charged at 0.3% per day of delay. If a resident's bill is R$580.00 and he pays that bill 15 days late, what will be the amount paid?
C = 580
i = 0.3% = 0.003
t = 15
M = ?
M = 580 (1 + 0.003). 15)
M = 580. 1,045
M = 606.10
The resident will have to pay BRL 606.10 by the water bill.
3) A debt of R$13,000 was paid 5 months after it was incurred and the interest paid was R$780.00. Knowing that the calculation was done using simple interest, what was the interest rate?
J = 780
C = 13 000
t = 5 months
i = ?
J = C. i. t
780 = 13 000. i. 5
780 = 65 000. i
i = 780/65,000
i = 0.012 = 1.2%
The interest rate is 1.2% per month.
4) A land whose price is R$ 100,000.00 will be paid in a single payment, 6 months after purchase. Considering that the rate applied is 18% per year, in the simple interest system, how much interest will be paid on this transaction?
C = 100,000
t = 6 months = 0.5 year
i = 18% = 0.18 per year
J = ?
J = 100,000. 0,5. 0,18
J = 9,000
Will be paid BRL 9,000 interest.
Contest Questions
1) UERJ- 2016
When purchasing a stove, customers can choose one of the following payment methods:
• in cash, in the amount of R$860.00;
• in two fixed installments of R$ 460.00, the first paid upon purchase and the second 30 days later.
The monthly interest rate for payments not made at the time of purchase is:
a) 10%
b) 12%
c) 15%
d) 18%
Alternative c: 15%
2) Fuvest - 2018
Maria wants to buy a TV that is being sold for R$1500.00 in cash or in 3 monthly interest-free installments of R$500.00. The money Maria set aside for this purchase is not enough to pay in cash, but she found that the bank offers a financial investment that earns 1% a month. After making the calculations, Maria concluded that if she pays the first installment and, on the same day, applies the remaining amount, you will be able to pay the two remaining installments without having to put or take a cent not even.
How much did Maria set aside for this purchase, in reais?
a) 1450.20
b) 1480.20
c) 1485.20
d) 1495.20
e) 1490.20
Alternative c: 1485.20
3) Vunesp - 2006
A school tuition payment slip, maturing on 08.10.2006, has a nominal value of R$740.00.
a) If the payment slip is paid by 07.20.2006, the amount to be charged will be R$703.00. What percentage of discount is granted?
b) If the bank slip is paid after 08.10.2006, interest of 0.25% will be charged on the face value of the bank slip, per day of delay. If paid 20 days late, how much will be charged?
a) 5%
b) BRL 777.00
4) Fuvest - 2008
On 12/08, Maria, who lives in Portugal, will have a balance of 2,300 euros in her checking account, and an installment of 3,500 euros to be paid, due on that day. Her salary is enough to pay off this installment, but it will be deposited in this checking account only on 12/10. Maria is considering two options to pay the installment:
1. Pay on the 8th. In this case, the bank will charge interest of 2% per day on the daily negative balance in your checking account, for two days;
2. Pay on the 10th. In this case, she will have to pay a fine of 2% of the total amount of the benefit.
Suppose there are no other transactions in your checking account. If Mary chooses option 2, she will have, in relation to option 1,
a) disadvantage of 22.50 euros.
b) advantage of 22.50 euros.
c) disadvantage of 21.52 euros.
d) advantage of 21.52 euros.
e) advantage of 20.48 euros.
Alternative c: 21.52 euros disadvantage
See too:
- Simple interest
- Compound interest
- Percentage
- Percentage Exercises
- Financial math
- Math Formulas
