Question

On January 1, 2012, Albert invested $6,000 at 8 percent interest per year for three years. The CPI (times 100) on January 1, 2012, stood at 100. On January 1, 2013, the CPI was 110 on January 1, 2014, it was 120; and on January 1, 2015, the day Albert’s investment matured, the CPI was 126. Find the real rate of interest earned by Albert in each of the three years and his total real return over the three-year period. Assume that interest earnings are reinvested each year and themselves earn interest.Hint: Calculate inflation and real interest for each year and then calculate it for the three years as a whole.Instructions: Enter your responses rounded to one decimal place. If you are entering any negative numbers be sure to include a negative sign (-) in front of those numbers.Year Real rate of interest2012 %2013 %2014 %Total real rate of return: __%.

Answer 1

Answer:

Inflation in 2012:

$=\frac{CPI\ 2013 - CPI\ 2012}{CPI\ 2012}$

$=\frac{110 - 100}{100}$

= 10%

Inflation in 2013:

$=\frac{CPI\ 2014 - CPI\ 2013}{CPI\ 2013}$

$=\frac{120 - 110}{110}$

= 9.09%

Inflation in 2014:

$=\frac{CPI\ 2015 - CPI\ 2014}{CPI\ 2014}$

$=\frac{126 - 120}{120}$

= 5%

Real rate of interest = Nominal - inflation

Given that,

Nominal rate = 8%

Therefore,

Real interest rate is as follows:

2012:

= 8% - 10%

= -2%

2013:

= 8% - 9.09%

= -1.09%

2014:

= 8% - 5%

= 3%

$6000 at 8% grows to:

= 1000 × 1.08

= $6,480 in one year

which is invested again to grow to $6,998.4 in two years

which is invested again to grow to $7,558.272 in three years

so,

Total gain:

$=\frac{7,558.272-6,000}{6000}\times100$

= 25.9712%

The price level increases in three years by:

$=\frac{CPI\ 2015 - CPI\ 2012}{CPI\ 2012}\times 100$

$=\frac{126 - 100}{100}\times 100$

= 26%

So,

Total real rate of return:

= Total gain - Percentage increase in prices

= 25.9712 - 26

= -0.0288%

Answer 2

Based on the CPI in various years and the interest rates, the real interest rates for the given years were:

• 2012 ⇒ -2%
• 2013 ⇒ -1.09%
• 2014 ⇒ 3%
• Total real interest rate of return = -0.029%.

What is the real interest rate in 2012?

= Interest rate invested - ( CPI in the next year - (CPI in current year / CPI in current year) )

= 8% - (110 - (100 / 100))

= -2%

What was the real interest rate in 2013?

= 8% - (120 - (110 / 110))

= -1.09%

What was the real interest rate in 2014?

= 8% - (126 - (120 / 120))

= 3%

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