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If John invested $ 1 at 5 percent interest compounded

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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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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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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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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

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