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

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swerve: Legendary Member; Posts: 2499; Joined: Sun Oct 29, 2017 2:04 pm; Followed by:6 members

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

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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Source: Beat The GMAT — Problem Solving | Fri Feb 23, 2018 7:37 am

DavidG@VeritasPrep: Legendary Member; Posts: 2663; Joined: Wed Jan 14, 2015 8:25 am; Location: Boston, MA; Thanked: 1153 times; Followed by:128 members; GMAT Score:770

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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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

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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