Question

Deondra is going to invest $64,000 and leave it in an account for 5 years. Assuming the interest is compounded quarterly, what interest rate, to the nearest hundredth of a percent, would be required in order for Deondra to end up with $82,000?

Answer 1

To the nearest hundredth of a percent, an interest rate of 6.68% would be required for Deondra to end up with $82,000 after 5 years of compounding interest.

Step-by-step explanation:

We can use the formula for compound interest to solve this problem:

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

where:

A = the final amount (in this case, $82,000)

P = the principal (the initial investment, in this case, $64,000)

r = the interest rate (what we're trying to find)

n = the number of times the interest is compounded per year (in this case, 4, since it's compounded quarterly)

t = the number of years (in this case, 5)

Plugging in the values we know and solving for r, we get:

$82,000 = $64,000(1 + r/4)^(4*5)

$82,000/$64,000 = (1 + r/4)^20

1.28125 = (1 + r/4)^20

Taking the 20th root of both sides, we get:

(1.28125)^(1/20) = 1 + r/4

0.0167 = r/4

r = 0.0668 (rounded to four decimal places)

Therefore, to the nearest hundredth of a percent, an interest rate of 6.68% would be required for Deondra to end up with $82,000 after 5 years of compounding interest.

Answer 2

Deondra needs to calculate the interest rate to grow $64,000 to $82,000 in 5 years with compound interest compounded quarterly. The formula A = P(1 + r/n)^(nt) is used, with A being the future value, P the principal, r the interest rate, n the number of compounding periods per year, and t the time in years. After finding the interest rate, it is rounded to the nearest hundredth of a percent.

Step-by-step explanation:

Deondra needs to find the appropriate interest rate that would grow her investment of $64,000 to $82,000 in 5 years, with the interest being compounded quarterly. To solve this, we can use the compound interest formula:

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 form).

n is the number of times that interest is compounded per year.

t is the time the money is invested for, in years.

In Deondra's case, A is $82,000, P is $64,000, n is 4 (since interest is compounded quarterly), and t is 5 years. We need to find the interest rate r. The equation to solve is:

82000 = 64000(1 + r/4)^(4*5)

Now, we need to solve for r:

(82000/64000) = (1 + r/4)^20

(1.28125) = (1 + r/4)^20

We can then use logarithms to solve for r, and then convert the decimal into a percentage, rounding to the nearest hundredth of a percent.

After solving the equation, we would find the required quarterly compounded interest rate to achieve Deondra's financial goal.