A bank offers the following choices for certificates of deposit:
| Term (in years) | Nominal annual interest rate convertible quarterly |
|---|---|
| 1 | 4.00% |
| 3 | 5.00% |
| 5 | 5.65% |
The certificates mature at the end of the term. The bank does NOT permit early withdrawals. During the next 6 years the bank will continue to offer certificates of deposit with the same terms and interest rates. An investor initially deposits 10,000 in the bank and withdraws both principal and interest at the end of 6 years.
Calculate the maximum annual effective rate of interest the investor can earn over the 6-year period.
References
Hlynka, Myron. "University of Windsor Old Tests 62-392 Theory of Interest". web2.uwindsor.ca. Retrieved November 23, 2023.
Solution: D
There are essentially four possible ways to invest for 6 years. (6=1+1+1+1+1+1=3+1+1+1=3+3=5+1). Just looking at the interest rates tells us that the best investment is 5+1 years. Then (1 + i)6 = (1 + 0565/4)20 = (1 + .04/4)4 so i = .0548
References
Hlynka, Myron. "University of Windsor Old Tests 62-392 Theory of Interest". web2.uwindsor.ca. Retrieved November 23, 2023.