Videos: Average and Effective Rates
Equivalent: Invest $100 in 2 accounts, the following year they have the same balance
Effective = Average Annual = j1
The humongous bank believes in offering its customers choices. A banker offers you two different options for your investments. The premium growth account offers interest at j2 = 10%. The accelerator account offers an effective rate of 10.25%. Which account is better?
Using the BAII Plus to convert Interest rates:
Complete the following table, with each row being equivalent rates:
| Effective | Semi-annual | Quarterly | Monthly |
| j1 = 12% | |||
| j2 = 8% | |||
| j4 = 10% | |||
| j12 = 6% |
3. Mortgages charge interest on a semi-annual basis but payments are usually made monthly. Change a mortgage rate of j2 = 7% to a rate compounded monthly.
4. Your credit card charges interest at 1.5% per month. Find the effective rate.
5. Premium Savings bonds have the following rates (all annual).
Year 1: 2% Year 2: 5% Year 3: 12% Year 4: 15% Year 5: 24%
(a) How much would a $1,000.00 investment be worth at the end of the fifth year?
(b) What effective rate was earned?
6. Your investments earn a 100% return in the first year and lose 50% in the second year. What is your effective rate of return over the two years?
7. A mutual fund had returns of 12% compounded monthly in the first year; 18% compounded annually in the second year; and 4% compounded quarterly in the third year.
What would a $1,000 investment 3 years ago be worth today?
What was the average rate (compounded monthly) of return earned?
The fund lost $100 in the fourth year – what was the average effective rate of return for the four years?
Chapter Attribution
Video chapter in Business Mathematics by Chris Kellman, Leslie Major, Don Mallory, Frank Gruen, and Amy Goldlist shared under a CC BY-NC license.
