Expression for compound or exponential growth

TL;DR

In this video, the instructor explains how to calculate the amount of money in a savings account after 15 years with 1.8% compound interest.

Transcript

• [Instructor] You put $3,800 in a savings account. The bank will provide 1.8% interest on the money in the account every year. Another way of saying that, the money in the savings account will grow by 1.8% per year. Write an expression that describes how much money will be in the account in 15 years. So let's just think about this a little bit. Le... Read More

Key Insights

• 💗 Compound interest grows the initial amount over time by adding the interest earned from each period.
• ☠️ The formula for compound interest includes the initial amount, growth rate, and the number of periods.
• 😑 The expression for one year can be used to calculate the amount in the account for any number of years.
• ⌛ Compound interest can result in significant growth over a long period of time.
• 💗 The exponent in the formula represents the number of years the amount is growing for.
• ❓ The formula for compound interest can be used to compare different investment options.
• 👻 Compound interest allows for exponential growth of savings over time.

Questions & Answers

Q: How is compound interest different from simple interest?

Compound interest is calculated based on the accumulated amount, including interest from previous periods, while simple interest is calculated only on the initial principal.

Q: Why is 1.8% expressed as 0.018 in the formula?

The decimal equivalent of 1.8% is 0.018, which is used to calculate the interest gained each year.

Q: What is the advantage of factoring out 3,800 from the expression?

Factoring out 3,800 simplifies the expression and allows for easier calculation by multiplying 3,800 by 1.018.

Q: How does the expression for one year apply to the expression for 15 years?

In each year, the amount grows by multiplying the previous amount by 1.018. This process is repeated 15 times to find the final amount in the account.

Summary & Key Takeaways

• The starting amount in the savings account is $3,800.

• Each year, the account grows by 1.8% of the previous amount.

• To find the amount in the account after 15 years, multiply the starting amount by 1.018 raised to the power of 15.