Simple and compound interest
An invested sum of money produces a profit: the interest. But not all banks calculate it in the same way. If the same amount is earned every year, it is simple interest; if the interest from one year is added to the capital and also earns interest the following year, it is compound interest. In the long run, the difference is enormous.
Simple interest
Calculate the simple interest produced by a principal of $3000$ € invested at $4\%$ per annum for $5$ years. What will be the final amount at the end of this period?
Calculate the simple interest produced by a principal of $3000$ € 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 $1500$ € 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…
A bank grants a loan of $1500$ € 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.
Compound interest
Calculate the final amount obtained by depositing $5000$ € into a savings account offering $3\%$ annual compound interest for $4$ years.
Calculate the final amount obtained by depositing $5000$ € into a savings account offering $3\%$ annual compound interest for $4$ years.
Compare the return on a principal of $8000$ € invested for $6$ years at a rate of $5\%$ per annum under two different methods: simple interest and compound interest.…
Compare the return on a principal of $8000$ € invested for $6$ years at a rate of $5\%$ per annum under two different methods: simple interest and compound interest. What is the exact difference in euros between the interest generated by both methods?
Finding the capital, rate or time
Find the principal initially invested at a simple interest rate of $5\%$ per annum if after $3$ years it generated $450$ € in profit.
Find the principal initially invested at a simple interest rate of $5\%$ per annum if after $3$ years it generated $450$ € in profit.
A principal of $2000$ € has grown to $2240$ € after remaining invested for $4$ years at simple interest. Find the annual interest rate applied.
A principal of $2000$ € has grown to $2240$ € after remaining invested for $4$ years at simple interest. Find the annual interest rate applied.
Set up the corresponding equation and use logarithms to determine how many years must elapse for a principal of $5000$ € to grow to $7000$ € if invested at an annual…
Set up the corresponding equation and use logarithms to determine how many years must elapse for a principal of $5000$ € to grow to $7000$ € if invested at an annual compound interest rate of $3,5\%$.
Depreciation: compound interest in reverse
A motorbike, a mobile phone or a computer loses value each year at a constant percentage rate: the same formula as compound interest, but subtracting instead of adding.
A new motorbike has a price of $4000$ €. If it loses $10\%$ of its value each year, calculate what its exact value will be after $3$ years.
A new motorbike has a price of $4000$ €. If it loses $10\%$ of its value each year, calculate what its exact value will be after $3$ years.
A mobile 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…
A mobile 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.
Two capitals, one equation
When two different investments must be made equal (the same final capital, or the same time), an equation is set up — sometimes with logarithms if both are compound.
Salma invests $3000$ € at $4\%$ per annum and Bruno invests $2500$ € at $6\%$ per annum, both at simple interest. Set up an equation and calculate in how many years they…
Salma invests $3000$ € at $4\%$ per annum and Bruno invests $2500$ € 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.
Carlos invests $4000$ € at an annual compound interest rate of $5\%$. On the same day, Diana invests $5000$ € at an annual compound interest rate of $3\%$. Use…
Carlos invests $4000$ € at an annual compound interest rate of $5\%$. On the same day, Diana invests $5000$ € 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.