MGF1131 ADVANCED MATHEMATICS
IN CONTEXT QUESTIONS AND
ANSWERS
1. A principal of $5,000 is invested at an annual interest rate of 6% compounded
continuously. What is the balance after 8 years?
A. $8,080.37
B. $7,400.00
C. $8,144.47
D. $8,053.86
Answer: A
Conceptual Explanation: The formula for continuous compounding is A = Pe^(rt). A =
5000 * e^(0.06 * 8) = 5000 * e^0.48 ≈ $8,080.37.
2. An investor contributes $200 at the end of each month into an annuity with a 5% interest
rate compounded monthly. How much is in the account after 25 years?
A. $119,101.62
B. $132,450.70
C. $120,000.00
,D. $139,040.68
Answer: D
Conceptual Explanation: The future value of an ordinary annuity formula is FV = PMT *
[((1 + r/n)^(nt) - 1) / (r/n)]. FV = 200 * [((1 + 0.05/12)^(12*25) - 1) / (0.05/12)] ≈
$139,040.68.
3. Compare the Effective Annual Yield (EAY) of two accounts: Account A offers 4.5%
compounded quarterly, and Account B offers 4.45% compounded daily (365 days).
A. Account A is better because its EAY is 4.58%
B. Account B is better because its EAY is 4.55%
C. Account A is better because its EAY is 4.50%
D. Both are exactly the same
Answer: A
Conceptual Explanation: EAY = (1 + r/n)^n - 1. For A: (1 + 0.045/4)^4 - 1 = 4.576%. For
B: (1 + 0.0445/365)^365 - 1 = 4.550%. A is higher.
4. A 30-year mortgage for $250,000 has a fixed interest rate of 4.2%. Calculate the total
interest paid over the life of the loan.
A. $189,840
B. $122,238
C. $439,840
, D. $197,320
Answer: A
Conceptual Explanation: Monthly payment M = P[i(1+i)^n]/[(1+i)^n - 1]. M =
250000[0.0035(1.0035)^360]/[(1.0035)^360 - 1] ≈ $1221.78. Total = (1221.78 * 360) -
250000 = $189,840.80.
5. If the price of a consumer basket was $150 in 2000 and the inflation rate averaged 3%
annually, what is the equivalent price in 2020?
A. $240.00
B. $285.31
C. $195.00
D. $270.92
Answer: D
Conceptual Explanation: Use the compound interest formula: A = P(1 + r)^t. A =
150(1.03)^20 ≈ $270.92.
6. A credit card calculates interest using the average daily balance method. If the balance was
$1,000 for 15 days and $2,000 for 15 days in a 30-day cycle, with a 24% APR, what is the
interest charge?
A. $60.00
B. $40.00
IN CONTEXT QUESTIONS AND
ANSWERS
1. A principal of $5,000 is invested at an annual interest rate of 6% compounded
continuously. What is the balance after 8 years?
A. $8,080.37
B. $7,400.00
C. $8,144.47
D. $8,053.86
Answer: A
Conceptual Explanation: The formula for continuous compounding is A = Pe^(rt). A =
5000 * e^(0.06 * 8) = 5000 * e^0.48 ≈ $8,080.37.
2. An investor contributes $200 at the end of each month into an annuity with a 5% interest
rate compounded monthly. How much is in the account after 25 years?
A. $119,101.62
B. $132,450.70
C. $120,000.00
,D. $139,040.68
Answer: D
Conceptual Explanation: The future value of an ordinary annuity formula is FV = PMT *
[((1 + r/n)^(nt) - 1) / (r/n)]. FV = 200 * [((1 + 0.05/12)^(12*25) - 1) / (0.05/12)] ≈
$139,040.68.
3. Compare the Effective Annual Yield (EAY) of two accounts: Account A offers 4.5%
compounded quarterly, and Account B offers 4.45% compounded daily (365 days).
A. Account A is better because its EAY is 4.58%
B. Account B is better because its EAY is 4.55%
C. Account A is better because its EAY is 4.50%
D. Both are exactly the same
Answer: A
Conceptual Explanation: EAY = (1 + r/n)^n - 1. For A: (1 + 0.045/4)^4 - 1 = 4.576%. For
B: (1 + 0.0445/365)^365 - 1 = 4.550%. A is higher.
4. A 30-year mortgage for $250,000 has a fixed interest rate of 4.2%. Calculate the total
interest paid over the life of the loan.
A. $189,840
B. $122,238
C. $439,840
, D. $197,320
Answer: A
Conceptual Explanation: Monthly payment M = P[i(1+i)^n]/[(1+i)^n - 1]. M =
250000[0.0035(1.0035)^360]/[(1.0035)^360 - 1] ≈ $1221.78. Total = (1221.78 * 360) -
250000 = $189,840.80.
5. If the price of a consumer basket was $150 in 2000 and the inflation rate averaged 3%
annually, what is the equivalent price in 2020?
A. $240.00
B. $285.31
C. $195.00
D. $270.92
Answer: D
Conceptual Explanation: Use the compound interest formula: A = P(1 + r)^t. A =
150(1.03)^20 ≈ $270.92.
6. A credit card calculates interest using the average daily balance method. If the balance was
$1,000 for 15 days and $2,000 for 15 days in a 30-day cycle, with a 24% APR, what is the
interest charge?
A. $60.00
B. $40.00
