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.
Bob invests 100 dollars in a fund that yileds 15% simple
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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
GMAT assassins aren't born, they're made,
Rich
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
GMAT assassins aren't born, they're made,
Rich
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Alternate approach: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
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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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.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
(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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