true or false?
Money in a bank account earning compound interest at an annual rate of 5% represents an example of linear growth?
I say True...
I would say false. It would grow exponentially because if it were linear, you would earn the same amount of interest every year. When you are talking compound interest, as it continues to be compounded year after year, you earn interest off of the interest you already earned. Sorry if I explained that poorly :p
False.
Money in a bank account earning compound interest at an annual rate of 5% represents an example of exponential growth, not linear growth. Linear growth occurs when a quantity increases by the same fixed amount over equal time intervals, whereas exponential growth occurs when a quantity increases by a fixed percentage over equal time intervals. In the case of compound interest, the interest earned each year is added to the initial amount, resulting in an exponential growth pattern.
False.
Money in a bank account earning compound interest at an annual rate of 5% does not represent linear growth. Linear growth refers to a constant increase over time, where the amount by which the quantity grows remains the same. In the case of compound interest, the growth is exponential, meaning the amount by which the account balance increases is not constant, but rather accumulates over time.
To understand this, you can use the compound interest formula: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount (initial deposit), r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.
For example, if you have $1,000 in a bank account earning compound interest at an annual rate of 5% compounded annually, after 1 year, your balance will be $1,050. However, after 2 years, your balance will not simply be $1,100 (twice the 5% interest of $50) but rather $1,102.50. This is because the interest earned in the second year is based on the new balance of $1,050, resulting in a slightly higher increase.
This compounding effect continues to grow over time, resulting in exponential growth rather than linear growth.