Simple interest
If you leave your money in a savings account, the bank pays you for using it. If you borrow money, you are the one who pays. This "rent on money" is called interest. Understanding it will help you decide where to save and avoid nasty surprises with a loan or an instalment plan.
The vocabulary of interest
| Word | Symbol | What it is |
|---|---|---|
| Principal | $C$ | The money you deposit or borrow |
| Interest rate | $r$ | The percentage that is paid each year |
| Time | $t$ | How long the deposit or loan lasts |
| Interest | $I$ | The money that is earned (or paid) |
| Final amount | $C_f$ | $C + I$ |
Through a banking app, Kofi sees that he has earned $15 €$ in interest in one year with a deposit paying $1,5 \%$ annual simple interest. What initial principal did Kofi…
Through a banking app, Kofi sees that he has earned $15 €$ in interest in one year with a deposit paying $1,5 \%$ annual simple interest. What initial principal did Kofi deposit one year ago to obtain that return?
The simple interest formula
With simple interest, you earn the same amount every year: $r\,\%$ of the initial principal.
Simple interest grows in a straight line (it is proportional to time). Compare it with compound interest, which you will see in the next section:
You have decided to save part of what you received for your birthday in a youth account offering $3 \%$ annual simple interest. If you deposit an initial principal of…
You have decided to save part of what you received for your birthday in a youth account offering $3 \%$ annual simple interest. If you deposit an initial principal of $400 €$ and keep the money in the bank for $2$ years, how many euros of interest will you have generated by the end of that time?
An investment platform for minors allows your parents to open a savings fund in your name. They have deposited $1500 €$ at $2,5 \%$ annual simple interest. If the money…
An investment platform for minors allows your parents to open a savings fund in your name. They have deposited $1500 €$ at $2,5 \%$ annual simple interest. If the money stays there for $4$ years until you start university, what will be the final amount in the account (the initial money plus interest)?
A youth association has deposited the proceeds from a charity fair, a total of $2400 €$, in a deposit account yielding $1,8 \%$ per annum. If they need to withdraw the…
A youth association has deposited the proceeds from a charity fair, a total of $2400 €$, in a deposit account yielding $1,8 \%$ per annum. If they need to withdraw the money after 100 days to fund a summer activity, how much interest will they have generated?
(Use the 360-day commercial year for the calculation).
Finding the principal, rate or time
With the same formula you can find any piece of data that is missing:
$$C = \frac{100 \cdot I}{r \cdot t} \qquad r = \frac{100 \cdot I}{C \cdot t} \qquad t = \frac{100 \cdot I}{C \cdot r}$$Marta has saved $200 €$ over $3$ years and the bank has paid her a total of $12 €$ in interest. At what annual interest rate was her money deposited?
Marta has saved $200 €$ over $3$ years and the bank has paid her a total of $12 €$ in interest. At what annual interest rate was her money deposited?
Calculate how long a principal of $1000 €$ must be deposited at an annual rate of $2 \%$ so that the interest produced is $60 €$. Express the result in years.
Calculate how long a principal of $1000 €$ must be deposited at an annual rate of $2 \%$ so that the interest produced is $60 €$. Express the result in years.
Lucía has decided to save the money she received at her 15th birthday party to go on an Interrail trip around Europe when she finishes school. She has deposited $2500$ €…
Lucía has decided to save the money she received at her 15th birthday party to go on an Interrail trip around Europe when she finishes school. She has deposited $2500$ € in a youth savings account that offers a simple interest rate of $3,5$ % per annum. If she plans to leave the money in the bank for exactly $3$ years, what interest will she earn to fund her trip?
Loans and fees
When you borrow money, you are the one who pays the interest. In addition, there are sometimes fees or withholdings: in Spain, the tax office keeps 19 % of the interest you earn in the bank.
You want to buy a new laptop and you are short of $600 €$. Your uncle lends you that money at a very low simple interest rate of $1,2 \%$ per annum, on condition that…
You want to buy a new laptop and you are short of $600 €$. Your uncle lends you that money at a very low simple interest rate of $1,2 \%$ per annum, on condition that you repay him in 6 months. Calculate the interest you will have to pay him at the end of that period.
(Remember to use the formula adapted for months: $I = \frac{C \cdot r \cdot t}{1200}$)
To upgrade its e-sports equipment, a local club has applied for a microcredit of $3600$ €. The provider applies a simple interest rate of $12$ % per annum. If the club…
To upgrade its e-sports equipment, a local club has applied for a microcredit of $3600$ €. The provider applies a simple interest rate of $12$ % per annum. If the club repays the money after $120$ days of competition, how much will the interest come to? (Use a $360$-day commercial year).
In Spain, bank interest is subject to a tax withholding rate of $19\%$. This means the bank retains $19\%$ of the profit (interest) and pays you the rest. If we deposit…
In Spain, bank interest is subject to a tax withholding rate of $19\%$. This means the bank retains $19\%$ of the profit (interest) and pays you the rest. If we deposit $8500 \text{ €}$ for $540$ days at an interest rate of $3,2\%$ per annum, what will be the net profit (after tax) we receive at the end of the period? Use a $360$-day commercial year.