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?
