Simple interest exercises

You simple interest are interest calculated without variation over time, that is, the value is always the same over the period. They can be applied to the starting capital on an annual, monthly, weekly or even daily basis.

THE formula for calculating simple interest é: J = C. i. t

Where:

J = simple interest

c = initial capital

i = interest rate

t = application time

already the formula for calculating the amount or final capital is: M = C + J

Where:

M = amount

C = initial capital

J = simple interest

Index

List of Simple Interest Exercises
Resolution of question 1
Resolution of question 2
Resolution of question 3
Resolution of question 4
Resolution of question 5
Resolution of question 6
Resolution of question 7
Resolution of question 8

List of Simple Interest Exercises

Question 1. How much interest will it earn:

a) the amount of R$ 1,800.00 applied for 10 months at a rate of 2.3% per month?

b) the amount of R$ 2,450.00 applied for 4 months at a rate of 1.96% per month?

Question 2. A rural producer took out a loan of R$ 5,200.00 and will pay it back in 5 months, at a rate of 1.5% per month.

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a) How much interest will this producer pay in the 5 months?

b) After 5 months, what is the total amount paid by the farmer?

Question 3. An investment of BRL 50,000 yielded, in 4 months, BRL 6,000.00 in interest. What is the monthly interest rate?

Question 4. Calculate the simple interest generated on a starting capital of $1,000 at a monthly rate of 3% for two years.

Question 5. Antônio borrowed R$7,000.00 and after four years, the amount borrowed was R$9,500.00. What was the interest rate applied?

Question 6. At a rate of 5% per year, how long will it take for a starting capital of $25,000 to convert to a closing capital of $30,000.00?

Question 7. Eva lent R$45,000.00 and at the end of 1 year, 4 months and 20 days she received R$52,500.00. What is the interest rate?

Question 8. A car costs R$ 22,000.00. A loan is granted to pay it back in 48 monthly installments at an annual rate of 6%. How much should be paid per month?

Resolution of question 1

a) We have to:

C = 1800

i = 2.3% = 2.3/100 = 0.023 per month

t = 10

Applying the simple interest formula:

J = C. i. t

J = 1800. 0,023. 10

J = 414

It will yield BRL 414.00.

b) We have to:

C = 2450

i = 1.96% = 1.96/100 = 0.0196 per month

t = 4

Applying the simple interest formula:

J = C. i. t

J = 2450. 0,0196. 4

J = 192.08

It will yield R$ 192.08.

Resolution of question 2

a) We have to:

C = 5200

i = 1.5% = 1.5/100 = 0.015 per month

t = 5

Applying the simple interest formula:

J = C. i. t

J = 5200. 0,015. 5

J = 390

Therefore, the producer will pay R$390.00 in interest.

b) We have to:

C = 5200

J = 390

Applying the amount formula, we have to:

M = C + J

M = 5200 + 390

M = 5590

So, after 5 months, the total paid by the producer will be R$ 5,590.00.

Resolution of question 3

We have:

C = 50000

J = 6000

t = 4 months

And we want to know the rate per month, that is, the value of i.

Applying the simple interest formula, we have to:

J = C.i.t

6000 = 50000.i.4

6000 = 200000.i

i = 6000/20000

i = 0.03

To get the percentage rate, we multiply by 100 and add the % symbol:

0.03 x 100% = 3%

Therefore, the monthly interest rate is equal to 3%.

Resolution of question 4

As the rate is applied to the month, we must also consider the total period in months. So let's write 2 years as 24 months.

So we have:

C = 1000

i = 3% = 3/100 = 0.03 per month

t = 24 months

Applying the simple interest formula, we have to:

J = C.i.t

J = 1000. 0,03. 24

J = 720

So, the interest generated over two years is R$720.00.

Resolution of question 5

The amount of BRL 7,000 is the initial capital and the amount of BRL 9,500.00 is the final capital, that is, the amount.

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So, we have to:

C = 7000

M = 9500

To determine the amount of interest, let's apply the amount formula:

M = C + J

9500 = 7000 + J

J = 9500 - 7000

J = 2500

This is the interest amount after 4 years. Now, to determine the rate, let's apply the simple interest formula:

J = C. i. t

2500 = 7000. i. 4

2500 = 28000.i

i = 2500/28000

i = 0.0893

To get the percentage rate, we multiply by 100 and add the % symbol:

0.0893 x 100% = 8.93%

Therefore, the rate is equal to 8.93% per year (since the period was given in years).

Resolution of question 6

We have to:

C = 25000

M = 30000

Let's apply the amount formula to figure out the interest amount:

M = C + J

30000 = 25000 + J

J = 30000 - 25000

J = 5000

Now we have to:

J = 5000

C = 25000

i = 5% = 5/100 = 0.05 per year

And we want to know the time t. Applying the simple interest formula:

J = C. i. t

5000 = 25000. 0,05. t

5000 = 1250.t

t = 5000/1250

t = 4

Therefore, it will take 4 years (since the rate was given in years) for the initial capital to be converted into R$30,000.

Resolution of question 7

We have to:

C = 45000

M = 52500

So, applying the amount formula:

M = C + J

52500 = 45000 + J

J = 52500 - 45000

J = 7500

It was not specified whether the interest rate should be per day, month or year, so we can choose.

We choose to specify the interest rate per day, so what we have to do is write the entire loan period in days.

1 year = 365

4 months = 120 days

365 + 120 + 20 = 505

In other words, 1 year, 4 months and 20 days equals 505 days.

So we have:

J = 7500

C = 45000

t = 505 days

And we want to find rate i. Applying the simple interest formula, we have to:

J = C.i.t

7500 = 45000. i. 505

7500 = 22725000.i

i = 7500/22725000

i = 0.00033

i = 0.033

To get the percentage rate, we multiply by 100 and add the % symbol:

0.00033 x 100% = 0.033%

Thus, the rate per day was 0.033%.

If by chance, we want to know the annual fee, just make a simple rule of three:

1 day — 0.00033

365 days — x

1.x = 0.00033. 365 ⇒ x = 0.12

So the annual rate is 12%.

Resolution of question 8

To find out how much will be paid per month, we must divide the amount, which corresponds to the value of the car plus the interest, by 48, which is the total number of months.

So we need to know the amount of the amount.

M = C + J

We have to:

C = 22000

i = 6% = 6/100 = 0.06 per year

t = 48 months = 4 years (we write it this way since the rate is annual)

But we don't have the value of J. Let's apply the simple interest formula to find out:

J = C.i.t

J = 22000. 0,06.4

J = 5280

Now that we know the interest amount, we can calculate the amount:

M = C + J