Exercises: Simple interest

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 $8{,}000$ pesos 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 $\$30\,000$ 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)?

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: $I = \frac{C \times r \times t}{1200}$)

A youth association has deposited the proceeds from a charity fair, a total of $\$48\,000$, 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).

Ximena has saved $4{,}000$ pesos over $3$ years and the bank has paid her a total of $240$ pesos in interest. At what annual interest rate was her money deposited?

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?

Imagine you have two options to keep $\$500$ from a prize for $2$ years:

• Option A: An account at $4 \%$ annual simple interest.

• Option B: An account that gives you a single payment of $\$35$ 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.

Calculate how long a principal of $\$20\,000$ must be deposited at an annual rate of $2 \%$ so that the interest produced is $\$1\,200$. 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 $2500$ 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?

A group of 9th-grade students (3° de secundaria) wants to buy a 3D printer for their technology project. The model they have chosen costs $24{,}000$ pesos. A financial institution offers them a loan at a simple interest rate of $4.2$ % per annum, to be repaid in $18$ months. Calculate how much money they will have to pay in interest at the end of that period.

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).

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 $3\,600$ 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 bank applying in this promotion?

Sara wants to buy an electric bicycle costing $30\,000$ pesos. She currently has $24\,000$ 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 $6\,000$ pesos, thus completing the amount she needs for the bicycle?

A young content creator has saved $100\,000$ 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. 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 $\$2450$. 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 $\$2450$ (counting their initial principal plus interest), how much money did they deposit initially?

A young entrepreneur of your age needs a loan of $\$24\,000$ to launch her online custom T-shirt shop. She has two options from financial institutions:

• Bank A: Offers her the money at a simple interest rate of $6\%$ per annum for $4$ years.

• 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 $\$300$.

Calculate how much total interest she will pay in each option and determine which one is the most economical for her.

Suppose that the bank withholds income tax (ISR) at a rate of $20\%$ on the interest earned. This means the bank retains $20\%$ of the profit (interest), pays it to the SAT, and pays you the rest. If we deposit $170{,}000$ pesos 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.

Daniela has split the $\$40\,000$ 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 $\$1\,840$, how much money did she invest in each product?

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.

A young athlete aged $18$ has just signed his first contract with a club, under which he will receive a bonus of $\$100\,000$ 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?