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. That "rental of money" is called interest. Imagine that Yaritza deposits 1,000 pesos at 3% per year: how much money will she have after 3 years? You're going to find out on this page.
The words of interest
| Word | Symbol | What it is |
|---|---|---|
| Principal | $C$ | The money you deposit or borrow |
| Interest rate (rate of return) | $r$ | The percentage paid each year (annual) |
| Time | $t$ | How long the deposit or loan lasts |
| Interest | $I$ | The money that is earned (or paid) |
| Final amount | $C_f$ | $C + I$ |
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 another 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 $\text{RD\$}\ 400$ and keep the money in the bank for $2$ years, how many pesos 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 $\text{RD\$}\ 90\,000$ at $2.5 \%…
An investment platform for minors allows your parents to open a savings fund in your name. They have deposited $\text{RD\$}\ 90\,000$ 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)?
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 $2500$ pesos 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?
When the time is in months or days
The rate is annual, so the time must be in years. If it is given to you in months or days, there are two ways: convert it to years, or use a different divisor.
You want to buy a new laptop and you are short of $\text{RD\$}\ 600$. Your uncle lends you that money at a very low simple interest rate of $1.2 \%…
You want to buy a new laptop and you are short of $\text{RD\$}\ 600$. 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: $I = \frac{C \times r \times t}{1200}$)
A youth association has deposited the proceeds from a charity fair, a total of $\text{RD\$}\ 144\,000$, in a deposit account yielding $1.8 \%…
A youth association has deposited the proceeds from a charity fair, a total of $\text{RD\$}\ 144\,000$, 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).
To upgrade its e-sports equipment, a local club has applied for a microcredit of $3600$ pesos. The provider applies a simple interest rate of $12$ % per annum. If the…
To upgrade its e-sports equipment, a local club has applied for a microcredit of $3600$ pesos. 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).
Solving for the principal and the interest rate
With the same formula you find whichever piece of data is missing. It is a first-degree equation: you solve for the letter you are looking for.
$$C = \frac{100 \times I}{r \times t} \qquad r = \frac{100 \times I}{C \times t} \qquad t = \frac{100 \times I}{C \times r}$$Through a banking app, Kofi sees that he has earned $\text{RD\$}\ 15$ in interest in one year with a deposit paying $1.5 \%…
Through a banking app, Kofi sees that he has earned $\text{RD\$}\ 15$ 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?
Marta has saved $\text{RD\$}\ 200$ over $3$ years and the bank has paid her a total of $\text{RD\$}\ 12$ in interest. At what annual interest rate was her money…
Marta has saved $\text{RD\$}\ 200$ over $3$ years and the bank has paid her a total of $\text{RD\$}\ 12$ in interest. At what annual interest rate was her money deposited?
Jorge's grandfather gave him a sum of money for passing all his subjects. Jorge invested that principal in a deposit account paying a simple interest rate of $3$ % per…
Jorge's grandfather gave him a sum of money for passing all his subjects. Jorge invested that principal in a deposit account paying a simple interest rate of $3$ % per annum. After $4$ years, the bank paid him $10\,800$ pesos in interest alone. What was the initial principal given by his grandfather?
A bank account for young entrepreneurs offers a return such that depositing $8000$ pesos for $3$ years yields $480$ pesos in interest. What annual interest rate is the…
A bank account for young entrepreneurs offers a return such that depositing $8000$ pesos for $3$ years yields $480$ pesos in interest. What annual interest rate is the bank applying in this promotion?
Solving for the time
Calculate how long a principal of $\text{RD\$}\ 60\,000$ must be deposited at an annual rate of $2 \%$ so that the interest produced is $\text{RD\$}\ 3\,600$. Express…
Calculate how long a principal of $\text{RD\$}\ 60\,000$ must be deposited at an annual rate of $2 \%$ so that the interest produced is $\text{RD\$}\ 3\,600$. Express the result in years.
Sara wants to buy an electric bicycle costing $90\,000$ pesos. She currently has $72\,000$ pesos and has deposited it in an account with a simple interest rate of $5$ %…
Sara wants to buy an electric bicycle costing $90\,000$ pesos. She currently has $72\,000$ pesos and has deposited it in an account with a simple interest rate of $5$ % per annum. How long (expressed in years) must she keep the money in the account so that the interest generated is $18\,000$ pesos, thus completing the amount she needs for the bicycle?
Calculate what annual interest rate a principal must be deposited at so that, after $15$ years, the interest earned is exactly equal to the initial principal deposited.…
Calculate what annual interest rate a principal must be deposited at so that, after $15$ years, the interest earned is exactly equal to the initial principal deposited. Does the result depend on the value of the principal chosen? Justify your answer mathematically.
Final amount and present value
Many problems talk about the total money, not just the interest. Since $C_f = C + I$ and $I = \dfrac{C\,r\,t}{100}$, you factor out $C$:
A young content creator has saved $300\,000$ pesos and decides to invest it in a financial product that guarantees a simple interest rate of $2.2$ % per annum for $5$…
A young content creator has saved $300\,000$ pesos and decides to invest it in a financial product that guarantees a simple interest rate of $2.2$ % per annum for $5$ years. Calculate the final amount (the sum of the initial principal plus interest) that the content creator will have at the end of the investment period.
A dance academy has bought a sound system worth $2400$ pesos. They have agreed to pay the amount in $10$ months' time with a surcharge of $6$ % annual simple interest.…
A dance academy has bought a sound system worth $2400$ pesos. They have agreed to pay the amount in $10$ months' time with a surcharge of $6$ % annual simple interest. What will be the total amount that the academy must pay in a single installment at the end of the $10$ months?
A group of friends wants to buy a professional sound system for their rehearsal space costing $\text{RD\$}\ 2450…
A group of friends wants to buy a professional sound system for their rehearsal space costing $\text{RD\$}\ 2450$. They have saved part of the money and decide to deposit it in an account that offers $4.5\%$ annual simple interest. Knowing that after $3$ years and $4$ months they have achieved exactly $\text{RD\$}\ 2450$ (counting their initial principal plus interest), how much money did they deposit initially?
A young athlete aged $18$ has just signed his first contract with a club, under which he will receive a bonus of $\text{RD\$}\ 300\,000…
A young athlete aged $18$ has just signed his first contract with a club, under which he will receive a bonus of $\text{RD\$}\ 300\,000$ upon completion. If the club decides to pay him that bonus today, but discounting the simple interest that this money would generate in an account at $3.5\%$ per annum over the remaining $6$ years of his contract, what amount will the athlete receive now?
Two investments with two rates
Sometimes the principal is split between two products with different rates and only the total interest is known. There are two unknowns, so you use a system of two linear equations (you will go deeper into this in the section on systems of equations).
Daniela has split the $\text{RD\$}\ 120\,000…
Daniela has split the $\text{RD\$}\ 120\,000$ she earned from her first summer job into two different financial products. The first offers a simple interest rate of $4\%$ per annum and the second a simple interest rate of $5\%$ per annum. If after one year she has obtained a total return of $\text{RD\$}\ 5\,520$, how much money did she invest in each product?
Loans, fees, and withholdings
When you borrow money, you are the one who pays the interest. Sometimes there is also a fee (a fixed payment for opening the loan). The total you pay is the interest plus the fee.
Withholding on interest
In some countries, part of the interest you earn is withheld as tax. The net gain is what you are left with: if $p\,\%$ is withheld, you collect $(100 - p)\,\%$ of the interest.
The withholding is applied to the interest earned, not to the principal, and it does not apply when you are the one paying interest on a loan.
Interest withdrawn each period
If the bank pays you interest every quarter and you withdraw it, the principal does not change and each quarter you earn the same amount: it is still simple interest. It only becomes "compound" if that interest is added to the principal and also earns interest (you will see this in another section).
Imagine you have two options to keep $\text{RD\$}\ 500$ from a prize for $2$ years: Option A: An account at $4 \%…
Imagine you have two options to keep $\text{RD\$}\ 500$ from a prize for $2$ years:
-
Option A: An account at $4 \%$ annual simple interest.
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Option B: An account that gives you a single payment of $\text{RD\$}\ 35$ interest at the end of the two years.
Calculate the interest for Option A and determine which of the two is more profitable for you.
A young entrepreneur of your age needs a loan of $\text{RD\$}\ 72\,000…
A young entrepreneur of your age needs a loan of $\text{RD\$}\ 72\,000$ to launch her online custom T-shirt shop. She has two options from financial institutions:
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Bank A: Offers her the money at a simple interest rate of $6\%$ per annum for $4$ years.
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Bank B: Offers her the same interest rate of $6\%$ per annum, but with a quarterly compounding of interest that she must withdraw each time (functioning as simple interest each quarter) over $48$ months. In addition, Bank B charges a fixed arrangement fee of $\text{RD\$}\ 900$.
Calculate how much total interest she will pay in each option and determine which one is the most economical for her.
In the Dominican Republic, 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…
In the Dominican Republic, 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 $\text{RD\$}\ 510\,000$ 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.