Question: On a certain day, Tim invested $1,000 at 10 percent annual interest, compounded annually, and Lana invested 2,000 at 5 percent annual interest, compounded annually. The total amount of interest earned by Tim’s investment in the first 2 years was how much greater than the total amount of interest earned by Lana’s investment in the first 2 years?

1. $5
2. $15
3. $50
4. $100
5. $105

Correct Answer: (A)
Solution with Explanation:

Approach Solution : 1

When interest is compounded annually, it is used once a year. One can choose to have 10% annual interest compounded daily, 10% annual interest compounded monthly (in which case 10%/12 would be applied each month), etc.
In accordance with the problem at hand,
Tim will have 1,000(1.10)^2 = 1,000(1.21) = 1,210 at the end of two years.
Lana will have 2,000(1.05)^2 = 2,000(1.1025) = 2,205
As a result, Tim had an earning of 210 dollars, while Lana had an earning 205 dollars
The difference is $5.

Approach Solution : 2

Following the first year, each person would have a 100 interest (10% of 1000 is100, and 5% of 2000 is 100)
The interest for both individuals is 100 for the following year.
The net interest is the difference between the interest that was added to both accounts.
Therefore, 10% of $100 equals $10 in additional interest for the account earning 10% interest.
and it is 5% of 100, which is 5, for the other account.
Therefore, the net difference is 10 - 5 = 5.

Approach Solution : 3

Let us do the calculations for Tim:
Interest for the first Year =100
Interest for the second Year = 110 (compounded)
Now, let us do the calculations for Lana:
Interest for the first Year =100
Interest for the second Year = 105 (compounded)
Therefore the difference is calculated as, 100 + 110 - (100 + 105) = 5

“On A Certain Day, Tim Invested $1,000 At 10 Percent Annual Interest, Compounded Annually GMAT Problem Solving” - is a subject covered in the GMAT quantitative reasoning section. A student needs to be knowledgeable in a wide range of qualitative skills in order to successfully complete GMAT Problem Solving questions. There are 31 questions in the GMAT Quant section overall. Calculative mathematical problems must be solved in the GMAT quant topics' problem-solving section using appropriate mathematical skills.

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