MGF1131 QUIZ 2: ADVANCED
MATHEMATICS IN CONTEXT
QUESTIONS AND ANSWERS
1. A principal of $5,000 is invested at an annual interest rate of 6% compounded monthly.
What is the balance after 10 years?
A. $9,096.98
B. $8,954.24
C. $9,103.45
D. $9,110.14
Answer: D
Conceptual Explanation: The formula is A = P(1 + r/n)^(nt). Here, A = 5000(1 +
0.06/12)^(12*10) = 5000(1.005)^120, which approximately equals $9,110.14.
2. Which of the following describes the Annual Percentage Yield (APY) if the Annual
Percentage Rate (APR) is 5.5% compounded daily?
A. 5.50%
B. 5.60%
C. 5.72%
,D. 5.65%
Answer: D
Conceptual Explanation: APY = (1 + r/n)^n - 1. For daily compounding (n=365), APY = (1
+ 0.055/365)^365 - 1 ≈ 0.0565 or 5.65%.
3. An investment doubles in value every 8 years. What is the approximate annual growth rate
using the Rule of 70?
A. 6.25%
B. 7.00%
C. 11.43%
D. 8.75%
Answer: D
Conceptual Explanation: Rule of 70 states doubling time ≈ 70 / growth rate. So, 8 = 70 / r,
which means r = = 8.75%.
4. A linear regression model shows a correlation coefficient (r) of -0.85. What percentage of
the variation in the dependent variable is explained by the independent variable?
A. 85.0%
B. 15.0%
C. 72.25%
D. 42.25%
, Answer: C
Conceptual Explanation: The coefficient of determination r^2 explains the variation. (-
0.85)^2 = 0.7225 or 72.25%.
5. In a normal distribution with a mean of 100 and a standard deviation of 15, what
percentage of values fall between 70 and 130?
A. 68%
B. 95%
C. 99.7%
D. 50%
Answer: B
Conceptual Explanation: According to the Empirical Rule, 95% of data falls within two
standard deviations (100 +/- 2*15 = 70 to 130).
6. Calculate the monthly payment for a 30-year fixed-rate mortgage of $250,000 at an
interest rate of 4.5%.
A. $1,266.71
B. $1,345.12
C. $1,125.00
D. $1,510.40
Answer: A
MATHEMATICS IN CONTEXT
QUESTIONS AND ANSWERS
1. A principal of $5,000 is invested at an annual interest rate of 6% compounded monthly.
What is the balance after 10 years?
A. $9,096.98
B. $8,954.24
C. $9,103.45
D. $9,110.14
Answer: D
Conceptual Explanation: The formula is A = P(1 + r/n)^(nt). Here, A = 5000(1 +
0.06/12)^(12*10) = 5000(1.005)^120, which approximately equals $9,110.14.
2. Which of the following describes the Annual Percentage Yield (APY) if the Annual
Percentage Rate (APR) is 5.5% compounded daily?
A. 5.50%
B. 5.60%
C. 5.72%
,D. 5.65%
Answer: D
Conceptual Explanation: APY = (1 + r/n)^n - 1. For daily compounding (n=365), APY = (1
+ 0.055/365)^365 - 1 ≈ 0.0565 or 5.65%.
3. An investment doubles in value every 8 years. What is the approximate annual growth rate
using the Rule of 70?
A. 6.25%
B. 7.00%
C. 11.43%
D. 8.75%
Answer: D
Conceptual Explanation: Rule of 70 states doubling time ≈ 70 / growth rate. So, 8 = 70 / r,
which means r = = 8.75%.
4. A linear regression model shows a correlation coefficient (r) of -0.85. What percentage of
the variation in the dependent variable is explained by the independent variable?
A. 85.0%
B. 15.0%
C. 72.25%
D. 42.25%
, Answer: C
Conceptual Explanation: The coefficient of determination r^2 explains the variation. (-
0.85)^2 = 0.7225 or 72.25%.
5. In a normal distribution with a mean of 100 and a standard deviation of 15, what
percentage of values fall between 70 and 130?
A. 68%
B. 95%
C. 99.7%
D. 50%
Answer: B
Conceptual Explanation: According to the Empirical Rule, 95% of data falls within two
standard deviations (100 +/- 2*15 = 70 to 130).
6. Calculate the monthly payment for a 30-year fixed-rate mortgage of $250,000 at an
interest rate of 4.5%.
A. $1,266.71
B. $1,345.12
C. $1,125.00
D. $1,510.40
Answer: A
