Practice Problem – Compound Interest

Practice Question

Intro to Finance
Time Value of Money
Compound Interest
Short Answer

Mr. Riyuzaki and Mr. Yagami are having an argument on which bank offers the best saving accounts. In fact, Mr. Riyuzaki believes that his bank offers a better package, and he deposits his money in a Bank of Osaka account which offers 5.7145% compounded 4 time(s) per year. On the other hand, Mr. Yagami deposits his money in a Bank of Okinawa account which offers 6.8733% compounded 12 time(s) per year. Is Mr. Riyuzaki right? That is, which bank offers the best savings account, and by how much?

Answer +
Correct Answer:
Mr. Riyuzaki is wrong, since his bank offers an effective annual rate of 5.8382% which is smaller than Mr. Yagami's effective annual rate of 7.0941%. The former is smaller by 1.256%.
Explanation +

Step 1: Highlight Relevant Information

  • Bank of Osaka: 5.7145% compounded quarterly (m = 4)
  • Bank of Okinawa: 6.8733% compounded monthly (m = 12)
  • To fairly compare, we must compute the Effective Annual Rate (EAR) for each.

Step 2: EAR Formula

EAR = (1 + (Quoted Rate / m))m − 1

Step 3: Compute EAR for Each Bank

  • EAROsaka = (1 + 0.057145 / 4)4 − 1 ≈ 5.8382%
  • EAROkinawa = (1 + 0.068733 / 12)12 − 1 ≈ 7.0941%

Step 4: Interpretation

  • Even though Bank of Osaka has a decent quoted rate, it’s compounded fewer times.
  • Mr. Yagami’s bank offers the better effective annual return.
  • Difference in EARs: 7.0941% − 5.8382% = 1.256%

Final Answer: Mr. Riyuzaki’s bank is worse by 1.256% in terms of effective annual return.