Test on Interest: simple and compound

Question 1: The general formula for compound interest compounded once per year, Gₙ = G₀ · (1 + i)ⁿ, calculates only the total interest earned after 'n' periods.

A. Yes

B. No

Explanation: The formula Gₙ = G₀ · (1 + i)ⁿ calculates the future value (Gₙ), which is the total amount after 'n' periods, not just the total interest earned. The interest earned would be Gₙ - G₀.

Question 2: According to the study materials, why is it crucial to compare the Effective Annual Rate (EAR) rather than solely the nominal interest rate when evaluating different financial products?

A. The nominal interest rate always reflects the actual annual return or cost, regardless of compounding frequency.

B. EAR accounts for the effect of compounding, allowing for an accurate comparison of financial products with different compounding frequencies.

C. The nominal interest rate is the only factor determining the total interest earned or paid over a long period.

D. Comparing nominal rates is sufficient if all products have the same stated annual interest rate.

Explanation: The study materials state that the Effective Annual Rate (EAR) is 'the actual annual rate of return earned on an investment or paid on a loan, taking into account the effect of compounding.' It further explains that EAR is 'particularly useful for comparing financial products that have different nominal interest rates and different compounding frequencies.' The nominal rate is the stated rate 'without considering compounding,' making it an unreliable comparison tool on its own. Therefore, comparing EARs is crucial for an accurate assessment of true returns or costs.

Question 3: Ignoring inflation when considering interest returns means that a positive nominal return could still result in a loss of purchasing power.

A. Yes

B. No

Explanation: Inflation erodes the purchasing power of money. Therefore, even if an investment shows a positive nominal interest rate, if the inflation rate is higher, the real rate of return would be negative, leading to a loss in purchasing power despite the nominal gain.

Question 4: The long-term growth potential of compound interest for savings is often underestimated.

A. Yes

B. No

Explanation: The study materials state that 'The long-term growth potential of compound interest is often underestimated. Even small, consistent investments can grow into substantial sums over decades due to exponential growth.'

Question 5: Based on the provided examples for the Rule of 72, how many years would it take for an investment to double if it earns an annual compound interest rate of 6%?

A. 9 years

B. 12 years

C. 6 years

D. 72 years

Explanation: The study material provides an example: 'If an investment earns an annual compound interest rate of 6%, how long will it take to double? Doubling Time ≈ 72 / 6 = 12 years.'