You have found three investment choices for a one year deposit: 10% APR compounded monthly, 10% APR compounded annually, and 9% APR compounded daily. Compute the EAR for each investment choice. Assume that there are 365 days in the year.
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To compute the Effective Annual Rate (EAR) for each investment choice, we need to use the following formula:
EAR = (1 + r/n)^n - 1
Where:
- r is the annual interest rate in decimal form
- n is the number of compounding periods per year
For the first investment choice, with a 10% APR compounded monthly:
- r = 0.10 (10% in decimal form)
- n = 12 (compounded monthly)
Using the formula:
EAR = (1 + 0.10/12)^12 - 1
To calculate this using a calculator:
1. Add the fraction by entering (0.10/12).
2. Add 1 to the result.
3. Raise this number to the power of 12.
4. Subtract 1 from the result.
For the second investment choice, with a 10% APR compounded annually:
- r = 0.10 (10% in decimal form)
- n = 1 (compounded annually)
Using the same formula:
EAR = (1 + 0.10/1)^1 - 1
For the third investment choice, with a 9% APR compounded daily:
- r = 0.09 (9% in decimal form)
- n = 365 (compounded daily)
Using the formula again:
EAR = (1 + 0.09/365)^365 - 1
By calculating each of these expressions, you will get the Effective Annual Rate (EAR) for each investment choice.