Your best taxable investment opportunity has an EAR of 4%. You best tax free investment opportunity has an EAR of 3%. If your tax rate is 30%, which opportunity provides the higher after tax interest rate?
To determine which investment opportunity provides a higher after-tax interest rate, you need to calculate the after-tax interest rates for both the taxable and tax-free investments.
First, let's calculate the after-tax interest rate for the taxable investment opportunity:
1. Calculate the taxable interest rate by dividing the EAR by (1 minus the tax rate):
Taxable interest rate = 4% / (1 - 0.30) = 4% / 0.70 = 5.71%
Next, let's calculate the after-tax interest rate for the tax-free investment opportunity:
1. Calculate the after-tax interest rate for the tax-free investment opportunity by multiplying the EAR by (1 minus the tax rate):
After-tax interest rate = 3% * (1 - 0.30) = 3% * 0.70 = 2.1%
Comparing the after-tax interest rates, we find that the taxable investment opportunity yields a higher after-tax interest rate of 5.71%, while the tax-free investment opportunity provides an after-tax interest rate of 2.1%. Therefore, the taxable investment opportunity has a higher after-tax interest rate in this scenario.