If John invested $ 1 at 5 percent interest compounded

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VJesus12: Legendary Member; Posts: 2276; Joined: Sat Oct 14, 2017 6:10 amFollowed by: 3 members

by VJesus12 » Tue Mar 27, 2018 2:41 am

If John invested $ 1 at 5 percent interest compounded annually, the total value of the investment, in dollars, at the end of 4 years would be

A. (1.5)^4
B. 4(1.5)
C. (1.05)^4
D. 1 + (0.05)^4
E. 1 + 4(0.05)

The OA is the option C.

Is not A the correct option? I'm confused. Help!!!!

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Source: Beat The GMAT — Problem Solving | Tue Mar 27, 2018 2:41 am

Vincen: Legendary Member; Posts: 2898; Joined: Thu Sep 07, 2017 2:49 pmFollowed by: 5 members; Thanked: 6 times

by Vincen » Tue Mar 27, 2018 5:52 am

VJesus12 wrote:If John invested $ 1 at 5 percent interest compounded annually, the total value of the investment, in dollars, at the end of 4 years would be

A. (1.5)^4
B. 4(1.5)
C. (1.05)^4
D. 1 + (0.05)^4
E. 1 + 4(0.05)

The OA is the option C.

Is not A the correct option? I'm confused. Help!!!!

Hi Vjesus12.

The formula to calculate the interest compound is: $$\left(\text{Principal}\ \text{Amount}\right)\cdot\left(1+R\right)^T$$ where R is the interest rate (expressed as 0.r) and T the time.

Therefore, in this case R=5% (r=0.05) and T=4. Hence, $$Investment=\left(1\right)\cdot\left(1+0.05\right)^4=\left(1.05\right)^4.$$ The correct answer is the option C .

PD: The option A would be correct if the interest rate was 50%.

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ErikaPrepScholar: Legendary Member; Posts: 503; Joined: Thu Jul 20, 2017 9:03 amFollowed by: 15 members; Thanked: 86 times; GMAT Score:770

by ErikaPrepScholar » Wed Mar 28, 2018 6:40 am

Be super careful whenever you have a percent less than 10 - there will always be a zero after the decimal. (e.g. 5% = 0.05, 2.2% = 0.022, etc.)

One way you can think about converting a percent into a decimal is dividing by 100. So 50% = 50/100 = 0.5, while 5% = 5/100 = 0.05.

It can also help to think logically about the size of the numbers. 5% is a pretty small percent, so we want a decimal that is also pretty small. 0.5 is half of 1 (pretty large), so it isn't a logical match - we want a much smaller decimal.

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swerve: Legendary Member; Posts: 2568; Joined: Sun Oct 29, 2017 2:04 pmFollowed by: 6 members

by swerve » Wed Mar 28, 2018 8:54 am

Hi Vjesus12,

simple interest = (principal)(1 + RT)
compound interest = (principal)(1 + RT)^T

Where R is the yearly interest rate and T is the number of years.

In this prompt, the answer choices show that we don't actually have to calculate anything, we just need to "format" the calculation correctly. Where told that the interest is COMPOUNDED ANNUALLY, so we need the compound interest formula, with a principal of $1, and R of 5% (we would "translate" as .05) and T of 4. We'd have Option C.

Regards!

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8188; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Wed Mar 28, 2018 10:15 am

VJesus12 wrote:If John invested $ 1 at 5 percent interest compounded annually, the total value of the investment, in dollars, at the end of 4 years would be

A. (1.5)^4
B. 4(1.5)
C. (1.05)^4
D. 1 + (0.05)^4
E. 1 + 4(0.05)

Using the compound interest formula we have:

1(1 + 0.05)^4

(1.05)^4

Answer: C

Scott Woodbury-Stewart
Founder and CEO
[email protected]

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