Practice and learn more about financial mathematics by following our step-by-step solved and commented exercises. Be prepared for school and university entrance exams, or even to better organize your personal finances.
Exercise 1 (Percentage)
Acquiring your own property is the goal of many people. As the cash value can require very high capital, an alternative is to resort to financing through banks and housing programs.
The value of the installments is usually proportional to the client's monthly income. Thus, the higher his income, the higher the installment he will be able to pay. Considering a negotiation in which the value established for the installment is R$1350.00, corresponding to 24% of his income, it can be determined that this client's income is
a) R$13,500.00
b) R$3,240.00
c) R$5,625.00
d) R$9,275.00
We must ask ourselves: 24% of what amount results in R$1350.00?
In mathematical language:
Therefore, the monthly income of such a client is R$5,625.00.
Exercise 2 (Successive increase and discounts)
Variation in product prices is a common practice in the market. Some products, such as fuels, are very susceptible to these changes, which can occur due to price fluctuations. international price of a barrel of oil, government decisions, pressure from shareholders, transportation costs, free competition, among others.
Consider that the price of gasoline suffered a certain increase, followed by a 4% reduction. After a few weeks, a new increase of 5%, accumulating a variation of 8.864%. It can be stated that the percentage value of the first adjustment was
a) 7%
b) 8%
c) 9%
d) 10%
To calculate a percentage increase, we multiply the original value by the digit one, followed by a comma and the rate of increase.
For the 5% increase, we multiply by 1.05.
The final increase rate was 8.864%, therefore, it represents an increase of 1.08864.
To calculate a percentage reduction, we multiply the original value by 1.00 minus the reduction rate.
For the 4% reduction, we multiply by 0.96, therefore, 1.00 - 0.04 = 0.96.
As the accumulated variation was 8.864%, we equate this rate to the product of increases and decreases.
Calling the first adjustment x, we have:
Therefore, it can be concluded that the first increase was 8%.
Exercise 3 (Simple interest)
The capital market is an investment option that moves enormous amounts every year. Financial institutions such as banks, brokers and even the government itself, sell bonds that yield a percentage amount, with determined rates and terms. Suppose that one of these bonds can be purchased for R$1200.00 each, with a fixed term of 18 months, under the simple interest system.
When purchasing three titles, the total redeemed will be R$4,442.40, having been the monthly fee
a) 1.7%
b) 0.8%
c) 2.5%
d) 1.3%.
In the simple interest system, the amount is the sum of the initial capital plus interest.
As the rate always applies to the same initial capital, every month, we have:
The capital value, multiplied by the rate and multiplied by the number of periods.
In this case:
C is the capital of R$1,200.00 x 3 = R$3,600.00.
M is the amount of R$4,442.40.
t is the time, 18 months.
i is the rate.
Thus, we have:
In percentage, just multiply by 100, so the monthly rate was 1.3%.
Exercise 4 (Compound interest)
Aiming to obtain an amount of at least R$12,000.00 in six months, capital was invested in the compound interest system at a monthly rate of 1.3%. To be able to complete the period with the stipulated total and applying the lowest possible capital, under these conditions, this capital must be
a) R$11,601.11.
b) R$ 11 111.11.
c) R$8,888.88.
d) R$ 10,010.10.
To determine the amount in an application in the compound interest system, we use the relationship:
We have the following data:
M = R$12,000.00 minimum.
i = 0.013
t = 6 months.
Isolating C in the equation, substituting the values and solving the calculations:
Approximating the power result to 1.08:
Exercise 5 (interest and functions)
An investment simulator built two functions based on the following initial conditions: the capital would be R$2000.00 and the annual rate would be 50%.
For the simple interest system, the function presented was:
In the compound interest system:
Considering five years of capital invested in compound interest, the minimum number of full years needed to obtain the same amount would be
a) 10 years
b) 12 years old
c) 14 years old
d) 16 years old
Considering five years in the compound interest system, we have:
Substituting this value into the investment function for simple interest, we have:
Therefore, at least 14 full years would be required.
Exercise 6 (equivalent rates)
A CDB (Bank Deposit Certificate) is a type of financial investment in which the customer lends money to the bank, receiving interest in return, under established conditions. Suppose a bank is offering a CDB with a gross yield (tax free) of 1% a. m. (per month), in the compound interest system.
Analyzing the proposal, a client decides that he can keep an amount in the bank for six months, obtaining a rate of
a) 6.00%
b) 6.06%
c) 6.15%
d) 6.75%
Since the interest system is compound, we cannot simply multiply the monthly rate by six.
The monthly rate relates to the rate for the contracted period for:
Where,
i6 is the rate equivalent to the 6-month period, im is the monthly rate, in this case 1%.n is the number of months, in this case 6.Changing the rate from percentage form to decimal number:
Substituting the values in the formula and carrying out the calculations considering up to the fourth decimal place:
To transform it into a percentage, simply multiply by 100.
Exercise 7 (Enem 2022)
In a store, the promotional price for a refrigerator is R$1,000.00 for payment in cash only. Its normal price, outside of the promotion, is 10% higher. When paying with a store credit card, a 2% discount is given on the normal price.
A customer decided to buy this refrigerator, choosing to pay with the store's credit card. She calculated that the amount to be paid would be the promotional price plus 8%. When informed by the store of the amount to be paid, according to her option, she noticed a difference between her calculation and the amount presented to her.
The value presented by the store, compared to the value calculated by the customer, was
a) R$2.00 less.
b) R$ 100.00 less.
c) R$200.00 less.
d) R$42.00 higher.
e) R$80.00 higher.
Promotional price = R$1000.00
Normal price = R$1100.00
Price with credit card (2% discount) = R$1078.00
1100. (1,00 - 0,02) = 1100. 0,98 = 1078
Price calculated by the customer (promotional plus 8%) = R$1080.00
1000. (1,00 + 0,08) = 1000. 1,08 = 1080
Therefore, the price informed by the store was R$2.00 lower.
Exercise 8 (UPE 2017)
Faced with the crisis the country is going through, a financial company offers loans to public servants charging only simple interest. If a person withdraws R$8,000.00 from this finance company, at an interest rate of 16% per year, how long will it take to pay R$8,320?
a) 2 months
b) 3 months
c) 4 months
d) 5 months
e) 6 months
In the compound interest system, the amount is equal to the principal plus interest. The interest value is the product between the capital, the rate and the investment time.
The rate of 16% per year can be converted into monthly by dividing by 12.
Replacing the values:
You can get more exercise with:
- Compound interest exercises with commented feedback
- Simple Interest Exercises
Learn more about financial mathematics:
- Financial math
- How to calculate percentage?
- Percentage
- Simple and Compound Interest
- Compound interest
ASTH, Rafael. Financial mathematics exercises with explained answers.All Matter, [n.d.]. Available in: https://www.todamateria.com.br/exercicios-de-matematica-financeira/. Access at:
See too
- Simple Interest Exercises (with answers and comments)
- Financial math
- 6 compound interest exercises with commented feedback
- Percentage Exercises
- Simple and Compound Interest
- Simple interest: formula, how to calculate and exercises
- Compound interest
- Percentage
