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Bob invests 100 dollars in a fund that yileds 15% simple

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by BTGmoderatorLU » Mon Aug 13, 2018 2:24 pm

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Source: Magoosh

Bob invests 100 dollars in a fund that yields 15% simple interest monthly. If Bob invests the principal in the middle of January, which is the first month will he have more than $200 total?

A. June
B. July
C. August
D. February
E. March

The OA is C.
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by [email protected] » Mon Aug 13, 2018 5:57 pm
Hi All,

We're told that Bob invests 100 dollars in the middle of January into a fund that yields 15% simple interest calculated monthly. We're asked for the first month in which the fund will have more than $200 total. This question involves the Simple Interest Formula, although you will likely find it useful to 'brute force' the Arithmetic:

Simple Interest = (Principle)(1 + (R)(T)) where R is the interest rate that T is the number of periods.

Here, the Principle = $100, R = .15 and T is the variable that we are solving for. If you solve for T, you'll have...

(100)(1.15T) = 200
1.15T = 2
T = 2/1.15

This is not a particularly 'nice' calculation, so you might find it easier to count '$15 increases' instead. Since we're calculating Simple Interest, each month will generate $15 in interest - and the total in the account will increase by $15 each month: $100 in January, $115 in February, $130 in March, etc..... $145, $160, $175, $190, $205 in August.

Final Answer: C

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by GMATGuruNY » Tue Aug 14, 2018 2:10 am
BTGmoderatorLU wrote:Source: Magoosh

Bob invests 100 dollars in a fund that yields 15% simple interest monthly. If Bob invests the principal in the middle of January, which is the first month will he have more than $200 total?

A. June
B. July
C. August
D. February
E. March
Alternate approach:

To earn exactly $100 in interest at rate of $15 earned each month, the number of months required = 100/15 = 20/3 = 6.66 months.
The smallest integer greater than 6.66 is 7.
Implication:
After 7 months, the total amount of interest will for the first time EXCEED $100, with the result that Bob will have more than $200.
January + (7 months) = August.

The correct answer is C.
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by Jeff@TargetTestPrep » Sat Aug 18, 2018 6:35 pm
BTGmoderatorLU wrote:Source: Magoosh

Bob invests 100 dollars in a fund that yields 15% simple interest monthly. If Bob invests the principal in the middle of January, which is the first month will he have more than $200 total?

A. June
B. July
C. August
D. February
E. March
For Bob to have a total of more than $200, he will need to earn more than $100 in interest. Since he earns $15 each month in (simple) interest, he needs at least 100/15 = 6.67 months to earn more than $100 in total interest. This rounds to 7 months, which takes him to August.

(Note that even if he counts exactly 6.67 months from the middle of January, he will reach mid-July for the 6th month, and then he must go an additional 0.67 months, which will also take him into August.)

Alternate Solution:

Let's keep track the amount of money he will have in each month since January, keeping in mind that 100 x 0.15 = $15 is earned each month since we are dealing with simple interest:

January: $100

February: 100 + 15 = $115

March: 115 + 15 = $130

April: 130 + 15 = $145

May: 145 + 15 = $160

June: 160 + 15 = $175

July: 175 + 15 = $190

August: 190 + 15 = $205

We can stop at August since the total is more than $200.

Answer: C

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