Test on Simple and compound interest

Question 1: In the compound interest formula, the variable 'k' represents the total number of compounding periods over the entire duration of the loan or investment.

A. Yes

B. No

Explanation: The study materials state that 'k' represents the 'Number of times interest is compounded per year'. The total number of compounding periods is represented by 'k·t'.

Question 2: According to the provided study materials, what is the definition of interest?

A. The initial amount of money borrowed or invested.

B. The cost of borrowing money or the reward for lending money.

C. The total amount after 't' years, including principal and accumulated interest.

D. The annual percentage at which the principal grows or is charged.

Explanation: The study materials define interest as 'the cost of borrowing money or the reward for lending money.' The other options describe the principal, future value, or the interest rate, but not the core definition of interest itself.

Question 3: For an investment of 1,000 USD at 5% annual interest for 3 years, compounded quarterly, the future value is calculated by multiplying 1,000 USD by (1.0125)¹².

A. Yes

B. No

Explanation: According to the study materials for Case 3: Compounded Quarterly, the future value (FV) is calculated as FV = 1,000 USD · (1 + 0.05/4)⁴·³ which simplifies to FV = 1,000 USD · (1.0125)¹². Therefore, multiplying 1,000 USD by (1.0125)¹² is indeed an intermediate step in determining the future value.

Question 4: The future value of 1,000 USD invested at 5% for 3 years, when compounded semi-annually, is 1,159.69 USD.

A. Yes

B. No

Explanation: According to the 'Case 2: Compounded Semi-Annually (k=2)' section, the calculation for 1,000 USD invested at 5% for 3 years with semi-annual compounding results in a Future Value (FV) of 1,159.69 USD.

Question 5: Based on the provided study materials, what is the total amount after 2 years if 1,000 USD is invested at a 5% annual interest rate, compounded annually?

A. 1,050.00 USD

B. 1,100.00 USD

C. 1,102.50 USD

D. 1,157.63 USD

Explanation: The comparison table in the study materials shows that for a 1,000 USD investment at 5% interest compounded annually, the total amount after 2 years is 1,102.50 USD. This is calculated as 1,000 USD ⋅ (1.05)².