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Pat invested x dollars in a fund that paid 8 percent...

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by swerve » Fri Feb 23, 2018 7:37 am
Pat invest x dollars in a fund that paid 8 percent annual interest, compounded annually. Which of the following represents the value, in dollars, of Pat's investment plus interest at the end of 5 years?

$$A.\ 5\left(0.08x\right)$$
$$B.\ 5\left(1.08x\right)$$
$$C.\ \left(1+5\left(0.08x\right)\right)x$$
$$D.\ 1.08^5\cdot x$$
$$E.\ \left(1.08x\right)^5$$

The OA is D.

Please, can any expert explain this PS question for me? I tried to solve it but I can't get the correct answer. I need your help. Thanks.
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by DavidG@VeritasPrep » Fri Feb 23, 2018 9:15 am
swerve wrote:Pat invest x dollars in a fund that paid 8 percent annual interest, compounded annually. Which of the following represents the value, in dollars, of Pat's investment plus interest at the end of 5 years?

$$A.\ 5\left(0.08x\right)$$
$$B.\ 5\left(1.08x\right)$$
$$C.\ \left(1+5\left(0.08x\right)\right)x$$
$$D.\ 1.08^5\cdot x$$
$$E.\ \left(1.08x\right)^5$$

The OA is D.

Please, can any expert explain this PS question for me? I tried to solve it but I can't get the correct answer. I need your help. Thanks.
The compound interest formula:

Total Value of Investment = P * (1 + r)^t
P: Principal
r: interest rate for period in question
t: number of times compounded

In this case:
P = x
r = .08
t = 5

Plug 'n chug: x * (1.08)^5. That's D
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by Scott@TargetTestPrep » Mon Jun 17, 2019 4:31 pm
swerve wrote:Pat invest x dollars in a fund that paid 8 percent annual interest, compounded annually. Which of the following represents the value, in dollars, of Pat's investment plus interest at the end of 5 years?

$$A.\ 5\left(0.08x\right)$$
$$B.\ 5\left(1.08x\right)$$
$$C.\ \left(1+5\left(0.08x\right)\right)x$$
$$D.\ 1.08^5\cdot x$$
$$E.\ \left(1.08x\right)^5$$
We can use the compound interest formula A = P(1 + r/n)^(nt) to solve the problem.

Here, P = x, r = 0.08, n = 1, and t = 5. Therefore, the amount of her investment in 5 years will be:

A = x(1 + 0.08/1)^(1(5))

A = x(1.08)^5

Answer: D

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