A Sum Of Money Put At 5 % Per Annum Amounts To Rs. 840 In 4 Years. What Will It Amount To In 5 Years At The Same Rate?

by ADMIN 119 views

A sum of money put at 5% per annum amounts to Rs. 840 in 4 years. What will it amount to in 5 years at the same rate?

Understanding the Problem

The problem involves calculating the future value of a sum of money invested at a certain interest rate. In this case, the interest rate is 5% per annum, and the initial amount is unknown. However, we are given that the amount grows to Rs. 840 in 4 years. We need to find out how much it will grow to in 5 years at the same interest rate.

Using the Compound Interest Formula

To solve this problem, we can use the compound interest formula:

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

Where:

  • A is the amount after n years
  • P is the principal amount (initial amount)
  • r is the annual interest rate (in decimal form)
  • n is the number of times the interest is compounded per year
  • t is the time in years

In this case, we are not given the principal amount (P), but we are given the amount after 4 years (A = Rs. 840). We can use this information to find the principal amount.

Finding the Principal Amount

We can rearrange the compound interest formula to solve for the principal amount (P):

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

We know that:

  • A = Rs. 840
  • r = 5% = 0.05 (in decimal form)
  • n = 1 (compounded annually)
  • t = 4 years

Substituting these values into the formula, we get:

P = 840 / (1 + 0.05/1)^(1*4) P = 840 / (1.05)^4 P = 840 / 1.21550625 P = Rs. 692.19

Calculating the Amount after 5 Years

Now that we have found the principal amount (P), we can use the compound interest formula to find the amount after 5 years:

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

We know that:

  • P = Rs. 692.19
  • r = 5% = 0.05 (in decimal form)
  • n = 1 (compounded annually)
  • t = 5 years

Substituting these values into the formula, we get:

A = 692.19 * (1 + 0.05/1)^(1*5) A = 692.19 * (1.05)^5 A = 692.19 * 1.27628125 A = Rs. 886.19

Conclusion

Therefore, the sum of money put at 5% per annum will amount to Rs. 886.19 in 5 years, given that it amounts to Rs. 840 in 4 years.

Key Takeaways

  • The compound interest formula can be used to calculate the future value of a sum of money invested at a certain interest rate.
  • The principal amount (initial amount) can be found using the compound interest formula, given the amount after a certain period of time.
  • The amount after a certain period of time can be calculated using the compound interest formula, given the principal amount and the interest rate.

Real-World Applications

  • The compound interest formula has numerous real-world applications, including calculating the future value of investments, loans, and savings accounts.
  • Understanding the compound interest formula can help individuals make informed decisions about their financial investments and savings.

Common Mistakes to Avoid

  • Failing to account for compounding interest can lead to inaccurate calculations and poor financial decisions.
  • Not considering the time value of money can result in missed opportunities for growth and savings.

Additional Resources

Q&A: Understanding Compound Interest

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 calculated using the formula: A = P(1 + r/n)^(nt), where A is the amount after n years, P is the principal amount, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the time in years.

Q: How does compound interest work?

A: Compound interest works by adding the interest earned in a given period to the principal amount, and then calculating the interest on the new total for the next period. This process is repeated over time, resulting in a snowball effect where the interest earned grows exponentially.

Q: What is the difference between simple interest and compound interest?

A: Simple interest is calculated only on the principal amount, whereas compound interest is calculated on both the principal amount and any accrued interest. This means that compound interest grows faster over time, especially in the long term.

Q: How can I calculate compound interest?

A: You can calculate compound interest using the formula: A = P(1 + r/n)^(nt), where A is the amount after n years, P is the principal amount, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the time in years. You can also use online compound interest calculators or financial software to make the calculation easier.

Q: What are the factors that affect compound interest?

A: The factors that affect compound interest include the principal amount, the annual interest rate, the number of times the interest is compounded per year, and the time in years. Additionally, the compounding frequency (e.g., monthly, quarterly, annually) and the interest rate type (e.g., fixed, variable) can also impact the compound interest calculation.

Q: How can I use compound interest to my advantage?

A: You can use compound interest to your advantage by investing in a high-yield savings account, certificate of deposit (CD), or other interest-bearing instruments. You can also take advantage of compound interest by making regular deposits into a savings account or investment portfolio.

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

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

  • Failing to account for compounding interest
  • Not considering the time value of money
  • Using the wrong interest rate or compounding frequency
  • Not taking into account any fees or taxes that may affect the interest earned

Q: How can I optimize my compound interest earnings?

A: You can optimize your compound interest earnings by:

  • Investing in a high-yield savings account or other interest-bearing instruments
  • Making regular deposits into a savings account or investment portfolio
  • Taking advantage of compound interest by using a compound interest calculator or financial software
  • Considering the impact of fees and taxes on your interest earnings

Q: What are some real-world applications of compound interest?

A: Some real-world applications of compound interest include:

  • Calculating the future value of investments, loans, and savings accounts
  • Determining the interest rate on a loan or credit card
  • Evaluating the effectiveness of a savings plan or investment strategy
  • Understanding the impact of inflation on the purchasing power of money

Q: How can I learn more about compound interest?

A: You can learn more about compound interest by:

  • Reading books or articles on personal finance and investing
  • Taking online courses or attending workshops on financial literacy
  • Using online compound interest calculators or financial software
  • Consulting with a financial advisor or planner