IP Practice DS SET – 2
DS: Interest & Growth – Level 2
1.
Which investment earned more interest over 2 years?
(1) Account A invested $1000 at 5% simple interest.
(2) Account B invested $1000 at 4% compound interest.
(1) Account A invested $1000 at 5% simple interest.
(2) Account B invested $1000 at 4% compound interest.
Solution (C):
(1) Interest A = \( 1000 \times 0.05 \times 2 = 100 \). No info on B.
(2) Interest B = \( 1000(1.04)^2 – 1000 = 1000(1.0816) – 1000 = 81.60 \). No info on A.
Combined: \( 100 > 81.60 \). A earned more. Sufficient.
2.
Is the annual interest rate \(r\) greater than 4%?
(1) A sum of money doubles in 15 years at simple interest rate \(r\).
(2) The interest earned in 1 year on $100 is \(r\) dollars.
(1) A sum of money doubles in 15 years at simple interest rate \(r\).
(2) The interest earned in 1 year on $100 is \(r\) dollars.
Solution (A):
(1) Doubling at SI means \( rt = 1 \). Here \( t=15 \).
\( 15r = 1 \implies r = 1/15 \approx 0.066 = 6.6\% \).
Is 6.6% > 4%? Yes. Sufficient.
(2) This just defines simple interest (\(100 \times r/100 = r\)). It gives no value for \(r\). Not sufficient.
3.
A population grows at a constant annual rate. What is the rate?
(1) The population was 1000 in 2010.
(2) The population was 1210 in 2012.
(1) The population was 1000 in 2010.
(2) The population was 1210 in 2012.
Solution (C):
(1) Gives \(P_0\) but no \(P_{final}\). Not sufficient.
(2) Gives \(P_{final}\) but no \(P_0\). Not sufficient.
Combined: \( 1210 = 1000(1+r)^2 \).
\( (1+r)^2 = 1.21 \implies 1+r = 1.1 \implies r = 10\% \). Sufficient.
4.
If $500 is invested, will the total amount exceed $600 after 2 years?
(1) The interest is simple interest.
(2) The annual interest rate is 12%.
(1) The interest is simple interest.
(2) The annual interest rate is 12%.
Solution (B):
(1) No rate given. Not sufficient.
(2) If interest is Simple: \( 500 \times 0.12 \times 2 = 120 \). Total = 620 (> 600).
If interest is Compound: \( 500(1.12)^2 = 627.2 \) (> 600).
Regardless of the type of interest (since positive rates yield CI > SI), the amount exceeds $600 in both cases. Sufficient.
5.
What is the principal amount \(P\)?
(1) The simple interest on \(P\) for 2 years at 5% is $100.
(2) The compound interest on \(P\) for 2 years at 5% is $102.50.
(1) The simple interest on \(P\) for 2 years at 5% is $100.
(2) The compound interest on \(P\) for 2 years at 5% is $102.50.
Solution (D):
(1) \( P \times 0.05 \times 2 = 100 \implies 0.1P = 100 \implies P = 1000 \). Sufficient.
(2) \( P(1.05)^2 – P = 102.50 \implies P(1.1025 – 1) = 102.50 \implies 0.1025P = 102.50 \implies P = 1000 \). Sufficient.
Score: 0 / 0