Data Sufficiency

Can someone help me solve this DS problem involving compound interest?

At the start of 1997, Jane invested a sum of money with a fixed rate of interest, compounded quarterly over 3 years. What was the rate of interest?

1) At the end of 1998, Jane had $12,500 in her account (principal and interest)

2) At the end of 1999, Jane had $13,800 in her account (principal and interest)

Would the answer be C, since we have two different equations with two unknown variables (P = principal and I = Interest rate)?

woodsy wrote:Can someone help me solve this DS problem involving compound interest?

At the start of 1997, Jane invested a sum of money with a fixed rate of interest, compounded quarterly over 3 years. What was the rate of interest?

2) At the end of 1999, Jane had $13,800 in her account (principal and interest)

Since the interest rate is fixed, the amount in the account is multiplied by the SAME FACTOR each year.
Let x = the value of this factor.
To determine the interest rate, we need to know the value of x.
Question stem, rephrased:
What is the value of x?

Statement 1: At the end of 1998, Jane had $12,500 in her account (principal and interest).
Since the amount in the account before the end of 1998 is unknown, x can be virtually ANY VALUE.
INSUFFICIENT.

Statement 2: At the end of 1999, Jane had $13,800 in her account (principal and interest).
Since the amount in the account before the end of 1999 is unknown, x can be virtually ANY VALUE.
INSUFFICIENT.

Statements combined:
Since the amount at the end of 1999 is x times the amount at the end of 1998, we get:
13,800 = (12,500)x.
x = 13800/12500.
SUFFICIENT.

The correct answer is C.

Mitch, thank you for your reply. I think your response clarified a point about compound interest that had previously escaped me. That the interest rate, regardless of how many times it is compounded and regardless of how many years over which it is applied, essentially remains the same from YEAR to YEAR, so long as this rate is FIXED. Do I have this correct? Thanks again.

GMATGuruNY wrote:

woodsy wrote:Can someone help me solve this DS problem involving compound interest?

At the start of 1997, Jane invested a sum of money with a fixed rate of interest, compounded quarterly over 3 years. What was the rate of interest?

2) At the end of 1999, Jane had $13,800 in her account (principal and interest)

Since the interest rate is fixed, the amount in the account is multiplied by the SAME FACTOR each year.
Let x = the value of this factor.
To determine the interest rate, we need to know the value of x.
Question stem, rephrased:
What is the value of x?

Statement 1: At the end of 1998, Jane had $12,500 in her account (principal and interest).
Since the amount in the account before the end of 1998 is unknown, x can be virtually ANY VALUE.
INSUFFICIENT.

Statement 2: At the end of 1999, Jane had $13,800 in her account (principal and interest).
Since the amount in the account before the end of 1999 is unknown, x can be virtually ANY VALUE.
INSUFFICIENT.

Statements combined:
Since the amount at the end of 1999 is x times the amount at the end of 1998, we get:
13,800 = (12,500)x.
x = 13800/12500.
SUFFICIENT.

The correct answer is C.

woodsy wrote:Mitch, thank you for your reply. I think your response clarified a point about compound interest that had previously escaped me. That the interest rate, regardless of how many times it is compounded and regardless of how many years over which it is applied, essentially remains the same from YEAR to YEAR, so long as this rate is FIXED. Do I have this correct? Thanks again.

Yes.
Each year the amount in the account will increase by the SAME PERCENTAGE.

To illustrate:
Let's say $10,000 is invested in an account that earns 20% interest compounded semi-annually (implying that the amount in the account increases by 10% every 6 months).

Amount in the account after the first 6 months = 10,000 + 10% of 10,000 = 11,000.
Amount in the account at the end of the first year = 11,000 + 10% of 11,000 = 12,100.
Percent increase from 10,000 to 12,100 = (12,000 - 10,000)/(10,000) = 21%.

Amount in the account after the next 6 months = 12,100 + 10% of 12,100 = 13,310.
Amount in the account at the end of the second year = 13,310 + 10% of 13,310 = 14,641.
Percent increase from 12,100 to 14,641 = (14,461 - 12,100)/(12,100) = 21%.

Each year, the amount in the account increases by the SAME PERCENTAGE (21%).