Kylie invested a certain amount of money at r% yearly interest

Question

﻿Kylie invested a certain amount of money at r% yearly interest compounded at the end of each year and the same amount of money at (r + 2)% yearly interest compounded at the end of each year. What was the amount of money that Kylie invested at the (r + 2)% yearly interest rate?

(1) At the end of 1 year, the investment at the (r + 2)% yearly interest rate earned $200 more than the investment at the r% yearly interest rate.

(2) r = 3

gmatophobia · Accepted Answer

Let's assume the amount Kylie invests = p

Statement 1

(1) At the end of 1 year, the investment at the (r + 2)% yearly interest rate earned $200 more than the investment at the r% yearly interest rate.

For the first year, the interest obtained via compound interest and the interest obtained via simple interest are the same.

Interest Obtained at the end of the first year :

Investment 1   :  \frac{p * 1 * r}{100}

Investment 2   :  \frac{p * 1 * (r+2)}{100}

Given

\frac{p * 1 * (r+2)}{100} - \frac{p * 1 * r}{100} = 200

\frac{2p}{100} = 200

We can find p. The statement alone is sufficient. We can eliminate B, C, and E.

Statement 1

(2) r = 3

Just by knowing the rate, we cannot find the principal amount.

The statement alone is not sufficient.

Option A

JeffTargetTestPrep · Answer

If x dollars was invested at r%, and x dollars was invested at (r + 2)%, then we need to answer the question:

x = ?

Statement One Alone:

=> At the end of 1 year, the investment at the (r + 2)% yearly interest rate earned $200 more than the investment at the r% yearly interest rate.

The following equation represents the relationship between the amounts of interest earned on the two investments:

x  = x(r/100) + 200
xr + 2x = xr + 20,000
2x = 20,000
x = $10,000

Statement one is sufficient. Eliminate answer choices B, C, and E.

Statement Two Alone:

=> r = 3

Since no information is given about any actual dollar amounts, we can’t answer the question. Statement two is not sufficient.

Answer: A

sayan640 · Answer

r will get cancelled out and hence Statement 1 only is sufficient . Nice C trap question.

lawyeroffduty · Answer

Isn't the value of r will be 10,000? I think you have mistakenly choosen simple interest as in the question, it was clearly stated that we need to find out the compound interest. Please clarify

Gemmie · Answer

Amount M: r% interest, compounded annually
Amount M: (r+2)% interest, compounded annually

Question : B = ?

Statement 1 :  M * \frac{r+2}{100} = 200 + M * \frac{r}{100}

=>  M * \frac{2}{100} = 200

=> Can find B

=> Sufficient

Statement 2 : r = 3

=> Insufficient

Answer is B

gagan03 · Answer

How are these interest SI when it is written that they are compounded annually and thus should be compound interest?

Bunuel · Answer

Since we are given information about the amount at the end of 1 year, no compounding has happened yet. Therefore, compound interest behaves the same as simple interest during that period.

bumpbot · Answer

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Kylie invested a certain amount of money at r% yearly interest

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