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An employee put $5,000.00 in a retirement account that offers 9% interest compounded annually. The employee makes no additional deposits or withdrawals. Which amount is closest to the interest the employee will have earned at the end of 5 years?
A) $229.09
B) $450.00
C) $2,250.00
D) $2,693.12

Respuesta :

sqdancefan

Answer:

D) $2693.12

Step-by-step explanation:

The account balance is multiplied by 1.09 each year, so at the end of 5 years, it has been multiplied by 1.53862395....

After subtracting the initial deposit amount, the remainder is the interest earned:

... $5000×(1.53862395 -1) = $5000×0.53862395 ≈ $2693.12

You can use the formula of calculating the amount resulted after interest compounded on principle amount.

The amount closest to the interest the employee will have earned at the end of 5 years is given by:

Thus, Option D: $2693.12 is correct.

What is the formula for calculating the resulted amount by compound interest?

[tex]A = P(1 + \dfrac{R}{100})^T[/tex]

where A = Amount after T years

P = initial amount

R = R% annual compound interest rate

T = T years of time for which amount was deposited.

Since employee puts $5,000 in retirement account, thus P = $5000

The time for which the amount was deposited is 5, thus T = 5

The rate of compound interest was 9% annually.

Thus,we have, by formula:

[tex]A = P(1 + \dfrac{R}{100})^T\\ \\ A= 5000(1+\dfrac{9}{100})^5\\ \\ A = 5000 \times 1.53862395 \approx \$7693.119[/tex]

Now, we have:
A = P + CI

or

CI = A - P

or

CI = $7693.12 - $5000 = $2693.12

Thus, the amount $2693.12 is closest to the interest the employee will have earned at the end of 5 years.

Thus, Option D: $2693.12 is correct.

Learn more about compound interest here:

https://brainly.com/question/4257530

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