Calculating the Amount in Year 3

Oct 13, 2025 by leolavanderia.com.br 81 views

Understanding the Problem

In this problem, we are given a table with the amount of money in each year, starting from year 1 with an initial amount of $100. The amount increases by 10% each year. We are asked to calculate the values for the amount in year 3 and year 4.

Calculating the Amount in Year 3

To calculate the amount in year 3, we need to apply the 10% increase to the amount in year 2. The amount in year 2 is $110, which is a 10% increase from the amount in year 1.

We can calculate the amount in year 3 using the formula:

Amount in year 3 = Amount in year 2 + (10% of Amount in year 2)

Substituting the values, we get:

Amount in year 3 = $110 + (10% of $110) Amount in year 3 = $110 + $11 Amount in year 3 = $121

Therefore, the value of $d$ is $121.

Calculating the Amount in Year 4

To calculate the amount in year 4, we need to apply the 10% increase to the amount in year 3.

We can calculate the amount in year 4 using the formula:

Amount in year 4 = Amount in year 3 + (10% of Amount in year 3)

Substituting the values, we get:

Amount in year 4 = $121 + (10% of $121) Amount in year 4 = $121 + $12.10 Amount in year 4 = $133.10

Therefore, the value of $e$ is $133.10.

Conclusion

In this problem, we calculated the values for the amount in year 3 and year 4 using the formula for compound interest. We found that the amount in year 3 is $121 and the amount in year 4 is $133.10.

Mathematical Formula

The formula for compound interest is:

A = P(1 + r/n)^(nt)

Where:

A is the amount of money accumulated after n years, including interest.
P is the principal amount (the initial amount of money).
r is the annual interest rate (in decimal).
n is the number of times that interest is compounded per year.
t is the time the money is invested for in years.

In this problem, we used the formula:

Amount in year 3 = Amount in year 2 + (10% of Amount in year 2) Amount in year 4 = Amount in year 3 + (10% of Amount in year 3)

Which is a simplified version of the compound interest formula.

Real-World Application

This problem has a real-world application in finance and economics. It can be used to calculate the future value of an investment, such as a savings account or a retirement fund. It can also be used to calculate the future value of a loan, such as a mortgage or a car loan.

Example Use Case

Suppose you have a savings account with an initial balance of $1000 and an annual interest rate of 10%. You want to know the balance after 5 years. Using the compound interest formula, we can calculate the balance as follows:

Balance after 5 years = $1000(1 + 0.10/1)^(1*5) Balance after 5 years = $1000(1 + 0.10)^5 Balance after 5 years = $1000(1.10)^5 Balance after 5 years = $1000 * 1.61051 Balance after 5 years = $1610.51

Therefore, the balance after 5 years is $1610.51.

Conclusion

Q: What is compound interest?

A: Compound interest is the interest earned on both the principal amount and any accrued interest over time. It is a powerful tool for growing your savings or investments, but it can also work against you if you have a loan or debt.

Q: How does compound interest work?

A: Compound interest works by applying a fixed interest rate to the principal amount and any accrued interest over a set period of time. The interest is then added to the principal amount, creating a snowball effect that can lead to significant growth over time.

Q: What are the benefits of compound interest?

A: The benefits of compound interest include:

Rapid growth: Compound interest can lead to rapid growth of your savings or investments over time.
Passive income: Compound interest can provide a steady stream of passive income, without requiring you to actively work for it.
Wealth creation: Compound interest can help you create wealth over time, by earning interest on your interest.

Q: What are the risks of compound interest?

A: The risks of compound interest include:

Debt accumulation: Compound interest can work against you if you have a loan or debt, leading to rapid accumulation of debt.
Inflation: Compound interest can be eroded by inflation, which can reduce the purchasing power of your money.
Market volatility: Compound interest can be affected by market volatility, which can lead to fluctuations in the value of your investments.

Q: How can I maximize the benefits of compound interest?

A: To maximize the benefits of compound interest, you can:

Start early: Start saving or investing early, to take advantage of the power of compound interest.
Be consistent: Be consistent in your savings or investments, to create a steady stream of interest.
Choose the right investments: Choose investments that offer high interest rates and low risk, to maximize your returns.
Avoid debt: Avoid debt, or pay off high-interest debt quickly, to avoid the negative effects of compound interest.

Q: How can I minimize the risks of compound interest?

A: To minimize the risks of compound interest, you can:

Understand the terms: Understand the terms of your loan or investment, including the interest rate and compounding frequency.
Monitor your accounts: Monitor your accounts regularly, to ensure that you are earning interest and not accumulating debt.
Diversify your investments: Diversify your investments, to reduce your risk and maximize your returns.
Seek professional advice: Seek professional advice, if you are unsure about how to manage your finances or investments.

Q: What are some common mistakes to avoid when using compound interest?

A: Some common mistakes to avoid when using compound interest include:

Not starting early: Not starting to save or invest early, which can lead to missed opportunities and reduced returns.
Not being consistent: Not being consistent in your savings or investments, which can lead to irregular returns and reduced growth.
Not choosing the right investments: Not choosing investments that offer high interest rates and low risk, which can lead to reduced returns and increased risk.
Not monitoring your accounts: Not monitoring your accounts regularly, which can lead to missed opportunities and reduced returns.

Q: What are some common uses of compound interest?

A: Some common uses of compound interest include:

Savings accounts: Compound interest can be used to grow savings accounts, such as high-yield savings accounts or certificates of deposit (CDs).
Investments: Compound interest can be used to grow investments, such as stocks, bonds, or mutual funds.
Retirement accounts: Compound interest can be used to grow retirement accounts, such as 401(k) or IRA accounts.
Loans: Compound interest can be used to calculate the interest on loans, such as mortgages or car loans.