Deondra Is Going To Invest $90,000 And Leave It In An Account. If The Interest Is Compounded Monthly, What Interest Rate, To The Nearest Hundredth, Is Required In Order For Deondra To End Up With $201,000?

Mar 13, 2025 by ADMIN 208 views

Deondra's Investment: Calculating the Required Interest Rate

In this article, we will explore the concept of compound interest and how it can be used to calculate the required interest rate for Deondra's investment. Compound interest is a type of interest that is calculated on both the initial principal and the accumulated interest from previous periods. This means that the interest earned in each period is added to the principal, so that the interest earned in the next period is calculated on the new, higher balance.

Compound interest can be calculated using the formula:

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

Where:

A is the future value of the investment
P is the principal amount (initial investment)
r is the annual interest rate (in decimal form)
n is the number of times that interest is compounded per year
t is the number of years that the money is invested for

In this case, Deondra is investing $90,000 and wants to know the interest rate required to reach a future value of $201,000. We will use the formula above to calculate the required interest rate.

We are given the following values:

P = $90,000 (initial investment)
A = $201,000 (future value)
n = 12 (compounded monthly)
t = 2 (years)

We need to solve for r, the annual interest rate. We can rearrange the formula to isolate r:

r = (A/P)^(1/(nt)) - 1

Plugging in the values, we get:

r = ($201,000/$90,000)^(1/(12*2)) - 1

To solve for r, we can use a calculator or a computer program to evaluate the expression. After plugging in the values, we get:

r ≈ 0.1414

This means that the annual interest rate required to reach a future value of $201,000 is approximately 14.14%.

To express the interest rate as a percentage, we can multiply by 100:

14.14% ≈ 14.14

In this article, we used the formula for compound interest to calculate the required interest rate for Deondra's investment. We found that the annual interest rate required to reach a future value of $201,000 is approximately 14.14%. This means that Deondra would need to earn an interest rate of at least 14.14% per year, compounded monthly, in order to reach her goal.

This calculation can be used in a variety of real-world scenarios, such as:

Calculating the interest rate required to reach a specific savings goal
Determining the interest rate needed to fund a large purchase
Evaluating the effectiveness of different investment strategies

To calculate the interest rate required to reach a specific future value, use the formula above and plug in the values.
To calculate the future value of an investment, use the formula above and plug in the values.
To calculate the interest rate required to reach a specific future value with a different compounding frequency, adjust the value of n accordingly.

Compound Interest Formula: A = P(1 + r/n)^(nt)
Annual Interest Rate: r = (A/P)^(1/(nt)) - 1

Q: What is compound interest? A: Compound interest is a type of interest that is calculated on both the initial principal and the accumulated interest from previous periods.
Q: How do I calculate the required interest rate for an investment? A: Use the formula above and plug in the values.
Q: What is the difference between annual and monthly compounding? A: Annual compounding means that interest is calculated once per year, while monthly compounding means that interest is calculated 12 times per year.
Deondra's Investment: Q&A

In our previous article, we explored the concept of compound interest and how it can be used to calculate the required interest rate for Deondra's investment. We found that the annual interest rate required to reach a future value of $201,000 is approximately 14.14%. In this article, we will answer some frequently asked questions related to compound interest and Deondra's investment.

A: Compound interest is a type of interest that is calculated on both the initial principal and the accumulated interest from previous periods. This means that the interest earned in each period is added to the principal, so that the interest earned in the next period is calculated on the new, higher balance.

A: To calculate the required interest rate for an investment, you can use the formula:

r = (A/P)^(1/(nt)) - 1

Where:

A is the future value of the investment
P is the principal amount (initial investment)
r is the annual interest rate (in decimal form)
n is the number of times that interest is compounded per year
t is the number of years that the money is invested for

A: Annual compounding means that interest is calculated once per year, while monthly compounding means that interest is calculated 12 times per year. Monthly compounding can result in a higher interest rate than annual compounding, since the interest is calculated more frequently.

A: The interest rate has a direct impact on the future value of an investment. A higher interest rate will result in a higher future value, while a lower interest rate will result in a lower future value.

A: Yes, you can use the formula above to calculate the future value of an investment with a different compounding frequency. Simply adjust the value of n accordingly.

A: The formula for calculating the future value of an investment is:

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

Where:

A is the future value of the investment
P is the principal amount (initial investment)
r is the annual interest rate (in decimal form)
n is the number of times that interest is compounded per year
t is the number of years that the money is invested for

A: Yes, you can use the formula above to calculate the interest rate required to reach a specific savings goal. Simply plug in the values and solve for r.

A: Simple interest is a type of interest that is calculated only on the initial principal, while compound interest is a type of interest that is calculated on both the initial principal and the accumulated interest from previous periods.

In this article, we answered some frequently asked questions related to compound interest and Deondra's investment. We hope that this information has been helpful in understanding the concept of compound interest and how it can be used to calculate the required interest rate for an investment.

This Q&A article can be used in a variety of real-world scenarios, such as:

Calculating the interest rate required to reach a specific savings goal
Determining the interest rate needed to fund a large purchase
Evaluating the effectiveness of different investment strategies

To calculate the interest rate required to reach a specific future value, use the formula above and plug in the values.
To calculate the future value of an investment, use the formula above and plug in the values.
To calculate the interest rate required to reach a specific future value with a different compounding frequency, adjust the value of n accordingly.

Compound Interest Formula: A = P(1 + r/n)^(nt)
Annual Interest Rate: r = (A/P)^(1/(nt)) - 1

Q: What is compound interest? A: Compound interest is a type of interest that is calculated on both the initial principal and the accumulated interest from previous periods.
Q: How do I calculate the required interest rate for an investment? A: Use the formula above and plug in the values.
Q: What is the difference between annual and monthly compounding? A: Annual compounding means that interest is calculated once per year, while monthly compounding means that interest is calculated 12 times per year.