3. You buy a certificate of deposit (CD) that pays a nominal rate of 12% annually. You
have a tax rate of 25%, so if the interest on this CD is taxable (which it may not be)
your after-tax nominal rate is (1 ñ 25%) • 12% = 9%. Since 10% equals .1, we can
rewrite the equation as: (1 ñ .25) • .12 = .09. For parts (A-C), the nominal rate is 12%,
annually and the after-tax nominal rate is 9%.
A. If the inflation rate is 6% and interest on this CD is not taxable, what is the
real interest rate on the CD? Hint: What is the relationship between the real rate of
interest and the nominal rate of interest? (2 points)
B. If the inflation rate is 6% and the interest on this CD is taxable, what is the
real interest rate on the CD? (2 points)
How do I figure out real interest rate? And what do they mean for the hint in question A? PLEASE HELP!!!
Well, let me put on my clown nose and try to make this explanation a bit more amusing for you!
To figure out the real interest rate, you need to take into account the inflation rate. The real interest rate is the nominal rate minus the inflation rate. So, let's do some calculations, my friend!
In question A, the inflation rate is 6% and the interest on the CD is not taxable. Since the nominal rate is 12% and the inflation rate is 6%, we can subtract the inflation rate from the nominal rate to find the real interest rate. That's like taking a slice of cake and removing some icing - the real interest rate is what's left! So, the real interest rate would be 12% - 6% = 6%.
Now, let's move on to question B. Here, the inflation rate is still 6%, but now the interest on the CD is taxable. Remember, the after-tax nominal rate is 9%. So, we can subtract the inflation rate from the after-tax nominal rate to find the real interest rate. Imagine your after-tax nominal rate as a pizza, and the inflation rate as a pesky fly you need to shoo away - what remains is the real interest rate! The calculation would be 9% - 6% = 3%.
I hope that clears things up! Just remember, when dealing with the real interest rate, you gotta subtract that sly inflation rate. Good luck, my friend, and may your financial calculations bring a smile to your face!
To calculate the real interest rate, you need to subtract the inflation rate from the nominal interest rate. The real interest rate represents the purchasing power of the investment after accounting for inflation.
For question A, where the interest on the CD is not taxable, the real interest rate can be calculated using the equation:
Real interest rate = Nominal interest rate - Inflation rate
Given that the nominal interest rate is 12% and the inflation rate is 6%, you can substitute the values into the equation:
Real interest rate = 12% - 6% = 6%
Therefore, the real interest rate on the CD, when the interest is not taxable and the inflation rate is 6%, is 6%.
As for the hint given in question A, it suggests that the relationship between the real interest rate and the nominal interest rate is that the real interest rate is obtained by subtracting the inflation rate from the nominal interest rate. In other words, the real interest rate represents the actual increase in purchasing power after accounting for the effects of inflation.
To calculate the real interest rate, you need to subtract the inflation rate from the nominal interest rate. The real interest rate represents the actual purchasing power of your investment after accounting for inflation.
Let's solve each part of the question:
A. If the interest on the CD is not taxable and the inflation rate is 6%, you can calculate the real interest rate using the formula: real interest rate = nominal interest rate - inflation rate.
In this case, the nominal interest rate is 12% annually, and the inflation rate is 6%. Substituting these values into the formula:
Real interest rate = 12% - 6%
= 0.12 - 0.06
= 0.06 or 6%
Therefore, the real interest rate on the CD, when the interest is not taxable and the inflation rate is 6%, is 6%.
The hint in question A is asking about the relationship between the real rate of interest and the nominal rate of interest. The real interest rate represents the true return on your investment in terms of purchasing power, while the nominal interest rate does not consider the effect of inflation. In this case, the hint is reminding you to subtract the inflation rate from the nominal rate to determine the real rate of interest.
B. If the interest on the CD is taxable and the inflation rate is 6%, you need to calculate the after-tax nominal rate first using the formula mentioned in the question: after-tax nominal rate = (1 - tax rate) * nominal interest rate.
Given a tax rate of 25% and a nominal interest rate of 12%, we can substitute these values into the formula:
After-tax nominal rate = (1 - 0.25) * 0.12
= 0.75 * 0.12
= 0.09 or 9%
Now that we have the after-tax nominal rate, we can calculate the real interest rate by subtracting the inflation rate:
Real interest rate = after-tax nominal rate - inflation rate
= 9% - 6%
= 0.09 - 0.06
= 0.03 or 3%
Therefore, the real interest rate on the CD, when the interest is taxable, and the inflation rate is 6%, is 3%.