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?
- $5
- $15
- $50
- $100
- $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.
Suggested GMAT Problem Solving Samples
- A Rectangular Box has Dimensions 12*10*8 Inches GMAT Problem Solving
- A Driver Completed the First 20 Miles of a 40-Mile Trip at an Average Speed of 50 Miles Per Hour GMAT Problem Solving
- The sum of three numbers is 98. If the ratio between first and second be 2:3 and between second and third be 5:8 GMAT Problem Solving
- How Many Three-Letter Words Can be Constructed Using All the 26 Letters of the English Alphabet GMAT Problem Solving
- A Car Travels from Mayville to Rome at an Average Speed of 30 miles per hour GMAT Problem Solving
- A Certain Sum of Money is Divided Among A, B and C such that A Gets One GMAT Problem Solving
- The Ratio of Boys to Girls in Class A is 1 to 4, and that in Class B is 2 to 5 GMAT Problem Solving
- The Maximum Mark in an Examination is 100 and the Minimum is 0 GMAT Problem Solving
- How Many Litres of Pure Alcohol Must be Added to a 100-litre Solution That is 20 Percent Alcohol GMAT Problem Solving
- For Any Four Digit Number, abcd, *abcd*= (3^a)(5^b)(7^c)(11^d) GMAT Problem Solving
- How Many Five Digit Numbers Can be Formed Using Digits 0, 1, 2, 3, 4, 5, Which Are Divisible By 3 GMAT Problem Solving
- An “Armstrong Number” is an n-Digit Number That is Equal to the Sum of the nth Powers GMAT Problem Solving
- A train crosses a bridge of length 500 m in 40 seconds and a lamp post on the bridge in 15 seconds GMAT Problem Solving
- A Train can Travel 50% Faster than a Car GMAT Problem Solving
- A rectangle is inscribed in a hexagon that has all sides of equal length and all angles of equal measure GMAT Problem Solving
- A Positive Integer Is Divisible by 9 If And Only If The Sum of Its Digits is Divisible By 9 GMAT Problem Solving
- The two lines are tangent to the circle GMAT Problem Solving
- In a Certain Population, There are 3 Times as Many People Aged Twenty-One or Under GMAT Problem Solving
- In How Many Different Ways can 3 Identical Green Shirts and 3 Identical Red Shirts be Distributed Among 6 Children GMAT Problem Solving
- The Interior of a Rectangular Carton is Designed by a Certain Manufacturer GMAT Problem Solving
- How Many Factors of 80 are Greater Than\(\sqrt80\)? GMAT Problem Solving
- If ‘A’ Can Complete a Task in 3 Hours and ‘B’ Can Complete the Same Task in 6 Hours GMAT Problem Solving
- If A Equals the Sum of the Even Integers from 2 to 20, Inclusive GMAT Problem Solving
- A Store Currently Charges The Same Price for Each Towel That It Sells. GMAT Problem Solving
- What is the Value of [ √ 7 + √ 29 − √ 7 − √ 29 ] 2 GMAT Problem Solving
- What is The Area of a Triangle with the Following Vertices GMAT Problem Solving
- The Product of the Five Smallest Two-Digit Prime Numbers GMAT Problem Solving
- The Square of 5^√2 =? GMAT Problem Solving
- Two Adjacent Angles of a Parallelogram are in the Ratio of 1:3 GMAT Problem Solving
- Which of The Following is a Perfect Cube? GMAT Problem Solving
- If a Right Angled Isosceles Triangle Has an Area of 2x^2 + 2x + ½. GMAT Problem Solving
- A number N^2 has 35 factors. How many factors can N have? GMAT Problem Solving
- If the Total Surface Area of a Cube is 24, What is the Volume of the Cube? GMAT Problem Solving
- There are 5,280 Feet in 1 Mile and 12 Inches in One Foot GMAT Problem Solving
- An Isosceles Right Triangle has an Area of 50. What is the Length of the Hypotenuse? GMAT Problem Solving
- A is Thrice as Good a Workman as B and Takes 10 days Less to do a Piece of Work GMAT Problem Solving
- 999,999^2−1 equals? GMAT Problem Solving
- Which of the following represents the largest 4 digit number GMAT Problem Solving
- The Lengths of the Sides of an Obtuse-Angled Triangle are x, y, and z, Where x, y and z are Integers GMAT Problem Solving
- If the expression sqrt2+2+2+2+ ... extends to an infinite number of roots GMAT Problem Solving
- How Many Different Lines Are Determined by 4 Distinct Points in a Plane If No 3 GMAT Problem Solving
- If The Diagonal of Rectangle Z is d, And The Perimeter of Rectangle Z is p GMAT Problem Solving
- 99,999^2−1^2 = ? GMAT Problem Solving
- How Many of The Three-Digit Numbers Are Divisible by 7? GMAT Problem Solving
- In a Camp, There is a Meal for 120 Men or 200 Children GMAT Problem Solving
- As Part Of a Game, Four People Each Must Secretly Choose an Integer Between 1 and 4 GMAT Problem Solving
- If Integer p is a Factor of 42, is p a Prime Number? GMAT Problem Solving
- A Triangle in the xy-Coordinate Plane Has Vertices With Coordinates (7, 0), (0, 8), and (20, 10) GMAT Problem Solving
- A Regular Hexagon is Inscribed in a Circle, What is the Ratio of the Area of the Hexagon GMAT Problem Solving
- What Is The Circumference Of The Semicircle In The Figure Shown? GMAT Problem Solving
Comments