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

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%