Buffy and Spike each invest $2,000 at different rates of interest, com

Question

Buffy and Spike each invest $2,000 at different rates of interest, compounded annually, and make no withdrawals. At the end of two years, Buffy's account balance was $2,880, which was $460 higher than Spike's balance.

In the table below, select a rate of interest earned by Buffy and a rate of interest earned by Spike that are consistent with the information above.

Sajjad1994 · Accepted Answer

Official Explanation

The word problem states that Buffy and Spike each invest $2,000 at different rates of interest, compounded annually, and make no withdrawals. It also states that at the end of two years, Buffy's account balance was $2,880, which was $460 higher than Spike's balance.

With the numbers provided, you can use the formula for calculating compound interest to find the interest rate earned by each account. However, since the problem provides numbers in the answer choices, an easier method is to Plug In The Answers. Since both accounts start with the same amount of money, start with the first answer choice and Plug In the interest rate to find the interest earnings after two years. The interest rate that results in a balance of $2,880 will be Buffy's; the rate that results in a balance of $2,420 (Buffy's balance less $460) will be Spike's.

Start with the first answer choice, 5%. Use the calculator to find that in the first year, the account would earn 5% interest on $2,000, or $100, and the account value would be $2,100 at the end of the first year. In the second year, the account would earn 5% interest on $2,100, or $105, and the account value at the end of the second year would be $2,205. (This can also be calculated as 2000 × 1.05 × 1.05) Therefore, this is not a correct response for either Buffy or Spike.

Do the same calculations for the second answer choice, 10%. At the end of the first year, the account value would be $2,200, and at the end of the second year, the account value would be $2,420. Therefore, 10% is the correct response for Spike.

The third answer choice, 15%, would provide an account value of $2,300 at the end of the first year and $2,645 at the end of the second year. $2,645 is not $460 more than either of the first two choices, so 15% is not the correct answer choice for Buffy.

The fourth answer choice, 20%, would generate 20% interest on $2,000, or $400, in the first year, and at the end of the first year, the account value would be $2,400. In the second year, the account would earn 20% of $2,400, or $480, and the account balance at the end of the second year would be $2,880. Therefore, 20% is the correct answer choice for Buffy, and no further testing of answer choices is necessary.

Answer:

Buffy: 20%
Spike: 10%

rvgmat12 · Answer

Buffy - 20% and Spike - 10%

2000*1.2*1.2=1.44*2000 = 2880

2000*1.1*1.1= 1.21*2000 = 2420

Difference = 460

Green2k1 · Answer

Buffy and Spike each invest $2,000 at different rates of interest, compounded annually, and make no withdrawals. At the end of two years, Buffy's account balance was $2,880, which was $460 higher than Spike's balance.

Buffy 
A= 2880 , P = 2000, T= 2 year , say rate is r% per annum
A= P(1+ r)^2 
After solving r = 20%

Spike
A= 2880-460 =2420 , P = 2000, T= 2 year , say rate is R% per annum
A= P(1+ R)^2 
After solving R = 10%

yashikaaggarwal · Answer

Becky's interest rate is 20%
Spike's interest rate is 10%

Explaination in picture:

wannabeMBA10 · Answer

Buffy: 20%
Spike: 10%

Posted from my mobile device

ktzsikka · Answer

Given that the principal of $2000 when compounded annually for 2 years yields the amount of $2880 and $2420 for Buffy and Spike respectively (Balance of buffy is $460 higher than Spike's balance).
We need to find what (i) b% for Buffy and (ii) s% for Spike, such that $2000 compounded annually for 2 years at b% and s% yields the amount of $2880 and $2420 respectively.
Method 1:
To solve this problem is to simply use the CI formula i.e A = P*(1+ r/100)^t , where P is the initial principal, r is the interest rate, and, t is the number of time periods.
Solving for Buffy : $ 2880 =2000*(1+b/100)^2$ will yield b = 20, and

Solving for Spike : $ 2420 = 2000*(1+s/100)^2$ will yield s = 10

Hence, rate of interest earned by Buffy, b% = 20% and rate of interest earned by Spike, s% = 10%.

Method 2
When values in question are easy to handle, we can simply use the brute force method - picking a logical value from the options and calculating Simple Interest twice to get to the final answer. Like in this case I first picked ROI as 20% (as I could see getting 288 by just doing a quick mental calculation). This turned out to be the ROI for Buffy. Now for Spike, ROI has to be less than that of Buffy's - so logically we have 3 values to choose from (10,11,12 as ROI of 5 will yield to very less amount). The practical choice should be the middle one i.e 11% as if by calculating S.I twice with ROI of 11% then voila! otherwise, we will get an amount X which will be either more or less than the desired amount of $2420. If X is more than $2420, your answer is 10% and if X is less than $2420, your answer is 13%.
In this case, solving for ROI of 11% will yield the final amount, X = $2464.2 which is clearly more than $2420. Hence answer is 10%.

Summarizing,
Rate of interest earned by Buffy = 20%, and
Rate of interest earned by Spike = 10%.

Nirmesh83 · Answer

Buffy -20%
Spike -10%

Sajjad1994 · Answer

Hello Everyone!

Following is the official answer of this question.

Buffy: 20%
Spike: 10%

Competition mode is off now. I will post OE later within few hours.

Sajjad1994 · Answer

Everyone does well here, good explanations overall but on top are by  ktzsikka  and  yashikaaggarwal

This is a medium-level question and how you approach this question matters the most.

PS: Keep in mind you can use a calculator during the IR section in the GMAT.

Good luck

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Buffy and Spike each invest $2,000 at different rates of interest, com

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