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Neko [114]
3 years ago
6

On January 1, 2012, Albert invested $6,000 at 8 percent interest per year for three years. The CPI (times 100) on January 1, 201

2, 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: __%.
Business
1 answer:
qaws [65]3 years ago
5 0

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%

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6 0
2 years ago
you lend a friend 10,000 dollars for which your friend will repay you 27,027 dollars at the end of 5 years. What interest rate a
Step2247 [10]

Answer:

The interest rate is "21.999%".

Explanation:

The given values are:

Amount lent,

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Amount repaid,

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Years (n),

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As we know,

⇒  Amount \ repaid = Amount \ lent\times (1+r)^n

On substituting the given values, we get

⇒                27,027=10,000\times (1+r)^5

⇒                  \frac{27,027}{10,000}=(1+r)^5

⇒                 2.7027=(1+r)^5

⇒                 1+r = (2.7027)^{(1/5)}

⇒                 1+r=1.21999

On subtracting "1" from both sides, we get

⇒          1+r-1=1.21999-1  

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5 0
3 years ago
Formula for average inventory ​
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3 years ago
Corona Company is owned equally by Maria, her sister Carlita, her mother, Gabriella, and her grandmother Olivia, each of whom ho
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Answer:

200 shares

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3 0
3 years ago
You are looking at a one-year loan of $12,000. The interest rate is quoted as 8.4 percent plus two points. A point on a loan is
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Answer:

Explanation:

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While the financial health of borrowers affects how good an interest rate they can get, larger economic factors and government financial policy affect the whole mortgage rate universe. You can boil it down to these five important factors. All represent basic rules of supply and demand in one form or another. It's a little technical, but learning these principles will give you a good way to think about what you're paying now and what could be coming

Answer a.

Effective Annual Rate of a loan is 8.92%

Answer b.

Effective Annual rate R is 12.27%

Answer is not affected by Loan amount as certain percentage of loan that is deducted as points.

Explanation:

Answer a  

Points deducted = 2 or 2%

April = 8.4%

Monthly rate (i)= 8.4%/12= 0.007

Months in a year = 12

Effective Annual Rate of a loan =( (1+(i/(1-points)))^months in year)-1

((1+(0.007/(1-2%)))^12)-1

=0.08916311096 or 8.92%

So Effective Annual Rate of loan is 8.92%

Answer b

quoted interest rate = 11.4%

Monthly rate (i)= 11.4%/12=0.0095

Months in year = 12

points deducted= 2 or 2%

EAR of loan =((1+(i/(1-points))) ^months in year)-1

((1+(0.0095/ (1-2%))) ^12)-1

=0.1227334817 or 12.27%

Answer is not affected by Loan amount as certain % of loan is deducted as points.

5 0
3 years ago
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