Calculating the Simple Interest

Oct 13, 2025 by miodeya.com 19 views

Introduction

In this problem, we are given that David invested $220 in a savings account that offers a 3% return on the investment. We need to calculate the value of David's investment after a certain period of time. To do this, we will use the concept of simple interest, which is calculated as the product of the principal amount, the interest rate, and the time period.

Calculating the Simple Interest

The formula for simple interest is:

Simple Interest = Principal x Rate x Time

In this case, the principal amount is $220, the interest rate is 3% or 0.03, and the time period is not specified. However, we can calculate the interest earned per year as follows:

Interest per year = Principal x Rate = $220 x 0.03 = $6.60

Calculating the Future Value of the Investment

The future value of the investment is the sum of the principal amount and the interest earned. Since the interest is compounded annually, we can calculate the future value as follows:

Future Value = Principal + Interest = $220 + $6.60 = $226.60

However, this is the interest earned in one year. To find the future value after a certain number of years, we need to multiply the interest earned per year by the number of years.

Calculating the Future Value after n Years

Let's assume that the interest is compounded annually for n years. The future value of the investment can be calculated as follows:

Future Value = Principal x (1 + Rate)^n = $220 x (1 + 0.03)^n = $220 x (1.03)^n

Solving for n

We are given that the value of David's investment will be at least $250. We can set up an equation to solve for n as follows:

$220 x (1.03)^n ≥ $250

To solve for n, we can divide both sides of the equation by $220:

(1.03)^n ≥ $250 / $220 (1.03)^n ≥ 1.1364

Now, we can take the logarithm of both sides of the equation to solve for n:

n ≥ log(1.1364) / log(1.03) n ≥ 14.21

Since n must be a whole number, we can round up to the nearest integer:

n ≥ 15

Conclusion

In this problem, we calculated the future value of David's investment after a certain number of years. We found that the value of the investment will be at least $250 after 15 years.

Answer

Q: What is the formula for simple interest?

A: The formula for simple interest is:

Simple Interest = Principal x Rate x Time

Q: How do I calculate the interest earned per year?

A: To calculate the interest earned per year, you can multiply the principal amount by the interest rate.

Interest per year = Principal x Rate

Q: What is the future value of an investment?

A: The future value of an investment is the sum of the principal amount and the interest earned.

Future Value = Principal + Interest

Q: How do I calculate the future value of an investment after a certain number of years?

A: To calculate the future value of an investment after a certain number of years, you can use the formula:

Future Value = Principal x (1 + Rate)^n

Q: What is the meaning of the exponent n in the formula?

A: The exponent n represents the number of years that the interest is compounded.

Q: How do I solve for n in the equation?

A: To solve for n, you can take the logarithm of both sides of the equation and then divide by the logarithm of the base.

n ≥ log(1 + Rate)^n / log(1 + Rate)

Q: What is the significance of the result n?

A: The result n represents the minimum number of years required for the investment to reach a certain value.

Q: Can I use this formula to calculate the future value of any investment?

A: Yes, you can use this formula to calculate the future value of any investment, as long as you know the principal amount, the interest rate, and the number of years.

Q: What if the interest rate is not a whole number?

A: If the interest rate is not a whole number, you can still use the formula to calculate the future value of the investment. Simply convert the interest rate to a decimal and plug it into the formula.

Q: Can I use this formula to calculate the future value of an investment with compound interest?

A: Yes, you can use this formula to calculate the future value of an investment with compound interest. Simply use the formula:

Future Value = Principal x (1 + Rate)^n

Q: What if I want to calculate the future value of an investment with monthly compounding?

A: If you want to calculate the future value of an investment with monthly compounding, you can use the formula:

Future Value = Principal x (1 + Rate/12)^12n

Q: Can I use this formula to calculate the future value of an investment with quarterly compounding?

A: Yes, you can use the formula:

Future Value = Principal x (1 + Rate/4)^4n

Conclusion

In this article, we have discussed the formula for simple interest and how to calculate the future value of an investment. We have also answered some frequently asked questions about the formula and its application.