Question

Juanita worked hard all year so that she could go to nursing school the following year.    She put her savings into a mutual fund that paid a nominal interest rate of 3 percent a year.    The CPI was 170 at the beginning of the year and 180 at the end of the year. What was the real interest rate that Juanita​ earned?

Answer 1

Answer:

Real Interest Rate = -2.7%

Explanation:

The formula to calculate the Real Interest rate is:

$r=(\frac{1+i}{1+p})-1$

Here,

r = Real Interest Rate

i = Nominal Interest Rate = 3% = 0.03

p = Rate of Inflation

We have the value of Nominal Interest Rate. Before using the formula we need to calculate the Rate of Inflation. We have the values of CPI at the beginning and end of the year. From these we can calculate the Inflation Rate. The formula to calculate the inflation rate is:

$p=\frac{CPI_{new}-CPI_{old}}{CPI_{old}} \times 100\%$

Using the values in this formula, we get:

$p=\frac{180-170}{170} \times 100\%\\\\ p=5.88\%$

Now we have all the values that we need to use. The values in the formula will be used in decimals, not in percentages. Substituting the values, we get:

$r=(\frac{1+0.03}{1+0.588} )-1\\\\ r=-0.027\\\\ r=-2.7\%$

Thus, the Real Interest Rate that Juanita earned is -2.7%. This shows that rate of Inflation is more than the Nominal Interest and the value of her savings actually decreased compared to the beginning of the year.