Calculating the Principal Investment Amount

Oct 13, 2025 by thesweetdesigns.com 141 views

**To the Nearest Dollar, How Much Money Would Lakisha Need to Put into an Account Earning 5% Compounded Annually in Order to Have $30,000 at the End of 20 Years?**

Understanding the Problem

To solve this problem, we need to use the formula for compound interest, which is given by:

A = P(1 + r)^n

Where:

A is the future value of the investment/loan, including interest
P is the principal investment amount (the initial deposit or loan amount)
r is the annual interest rate (in decimal form)
n is the number of years the money is invested or borrowed for

In this case, we are given the future value (A) as $30,000, the annual interest rate (r) as 5% or 0.05, and the number of years (n) as 20. We need to find the principal investment amount (P).

Calculating the Principal Investment Amount

To find the principal investment amount (P), we can rearrange the formula for compound interest to solve for P:

P = A / (1 + r)^n

Plugging in the values given in the problem, we get:

P = 30000 / (1 + 0.05)^20

Using a Calculator or Spreadsheet to Find the Answer

To find the answer, we can use a calculator or spreadsheet to evaluate the expression:

P = 30000 / (1 + 0.05)^20 P ≈ 30000 / 3.3863 P ≈ 8901.19

Therefore, to the nearest dollar, Lakisha would need to put approximately $8901 into an account earning 5% compounded annually in order to have $30,000 at the end of 20 years.

Q&A

Q: What is the formula for compound interest? A: The formula for compound interest is A = P(1 + r)^n, where A is the future value of the investment/loan, including interest, P is the principal investment amount, r is the annual interest rate, and n is the number of years the money is invested or borrowed for.

Q: How do I calculate the principal investment amount? A: To calculate the principal investment amount, you can rearrange the formula for compound interest to solve for P: P = A / (1 + r)^n.

Q: What is the annual interest rate in decimal form? A: The annual interest rate in decimal form is 0.05, which is equivalent to 5%.

Q: How many years is the money invested or borrowed for? A: The money is invested or borrowed for 20 years.

Q: What is the future value of the investment/loan? A: The future value of the investment/loan is $30,000.

Q: What is the principal investment amount? A: The principal investment amount is approximately $8901.

Q: How do I use a calculator or spreadsheet to find the answer? A: To find the answer, you can use a calculator or spreadsheet to evaluate the expression: P = 30000 / (1 + 0.05)^20.

Q: What is the approximate value of the principal investment amount to the nearest dollar? A: The approximate value of the principal investment amount to the nearest dollar is $8901.

Conclusion

In this article, we have discussed how to calculate the principal investment amount using the formula for compound interest. We have also provided a step-by-step solution to the problem and answered some frequently asked questions. We hope that this article has been helpful in understanding the concept of compound interest and how to use it to solve problems.