Exercises: Simple and compound interest

Calculate the simple interest produced by a principal of $60\,000$ pesos invested at $4\%$ per annum for $5$ years. What will be the final amount at the end of this period?

A bank grants a loan of $30\,000$ pesos at $6\%$ annual simple interest. If the loan is repaid over a period of $8$ months, determine the total amount that must be paid to the bank as interest.

Calculate the final amount obtained by depositing $100\,000$ pesos into a savings account offering $3\%$ annual compound interest for $4$ years.

Find the principal initially invested at a simple interest rate of $5\%$ per annum if after $3$ years it generated $9\,000$ pesos in profit.

A new motorbike has a price of $80\,000$ pesos. If it loses $10\%$ of its value each year, calculate what its exact value will be after $3$ years.

A principal of $40\,000$ pesos has grown to $44\,800$ pesos after remaining invested for $4$ years at simple interest. Find the annual interest rate applied.

A cell phone battery loses $15\%$ of its charge for every hour of gaming. If you start playing with $100\%$ charge, determine what percentage of battery will remain after $5$ hours.

Calculate the simple interest generated by $200\,000$ pesos invested at $2.5\%$ per annum for $146$ days. Assume a year has $365$ days to perform the calculations.

Compare the return on a principal of $160\,000$ pesos invested for $6$ years at a rate of $5\%$ per year under two different methods: simple interest and compound interest. What is the exact difference in pesos between the interest generated by both methods?

A person wishes to have $200\,000$ pesos in $5$ years to buy a vehicle. If their bank offers a deposit with $4\%$ annual compound interest, how much money must they deposit today to achieve their goal exactly?

An initial principal of $120\,000$ pesos has grown to $142\,922$ pesos after $3$ years of investment. Knowing that the interest has been reinvested each year (compound interest), determine the annual interest rate applied.

An amount of $80\,000$ pesos is invested at a simple interest rate of $3\%$ per annum for $4$ years. After that time, the total final amount is withdrawn and reinvested in another financial product offering $4\%$ annual compound interest for $2$ more years. Calculate the overall final amount that will be obtained at the end of the $6$ years.

Determine how many years a principal must remain invested at a simple interest rate of $8\%$ per annum for its value to double.

An investor deposits $100\,000$ pesos at an annual compound interest rate of $6\%$, but with monthly compounding periods. Calculate the final amount they will have in their account after $2$ years.

A family spends $24\,000$ pesos per month on food. If the average inflation is estimated at $2.5\%$ per year, how much will they spend per month in $4$ years to maintain exactly the same level of consumption? Assume that price increases follow the compound interest formula.

Salma invests $3000$ pesos at $4\%$ per annum and Bruno invests $2500$ pesos at $6\%$ per annum, both at simple interest. Set up an equation and calculate in how many years they will have exactly the same accumulated final amount.

Set up the corresponding equation and use logarithms to determine how many years must elapse for a principal of $100\,000$ pesos to grow to $140\,000$ pesos if invested at an annual compound interest rate of $3.5\%$.

A person deposits $40\,000$ pesos into an account offering $4\%$ annual compound interest. After exactly $2$ years, they make a new deposit of $30\,000$ pesos into the same account. If they make no withdrawals, calculate the total accumulated amount they will have after $5$ years from the first deposit.

To finance a project, a company evaluates two loan options for an amount of $200\,000$ pesos to be repaid in a single payment after $3$ years. Bank A offers a simple interest rate of $6\%$ per year, but charges an origination fee of $1.5\%$ on the principal, paid at the time of granting. Bank B offers a compound interest rate of $5\%$ per year with no fee. Determine which option is cheaper at the end of the period and what the difference in pesos is between both.

Calculate what annual compound interest rate must be applied to a principal for its value to triple in exactly $15$ years. Express the result as a percentage rounded to two decimal places.

Carlos invests $80\,000$ pesos at an annual compound interest rate of $5\%$. On the same day, Diana invests $100\,000$ pesos at an annual compound interest rate of $3\%$. Use logarithms to determine after how many years the accumulated amount for Carlos will equal Diana's.

A high-end computer system currently costs $30\,000$ pesos. Due to technological obsolescence, its nominal value depreciates by $15\%$ each year. At the same time, inflation causes money to lose $2\%$ of its purchasing power annually. Calculate what the real value (adjusted for the loss of purchasing power) of the system will be after $4$ years.

An investor wishes to accumulate a final amount of $400\,000$ pesos in $4$ years. To achieve this, they plan to make an initial deposit of an amount $C$ today, and a second deposit of the same amount $C$ in exactly $2$ years. If the bank account offers a yield of $3\%$ annual compound interest, set up the corresponding equation and find the value of the contribution $C$.

The following graph shows the evolution of the same initial principal invested at simple interest (blue bars) and compound interest (green bars) with the same annual interest rate over the first three years. By observing the exact values on the graph, deduce the initial principal and the interest rate. Next, calculate what the exact difference in pesos between both methods will be after $10$ years.