<u>Given:</u>
Consumer price index in 1991 = 136.2
Consumer price index in 2017 = 244
One billion dollar in numbers = 1,000,000
<u>To find:</u>
Money required in 2017 to have the same amount of real purchasing power that they did in 1991.
<u>Solution:</u>
Assuming 1991 as base year and 2017 as target year,
The purchasing power during 1991-2017 is
![\Rightarrow\text { 1,000,000 } \times \frac{\text { CPI of target year }}{\text { CPI of base year }}](https://tex.z-dn.net/?f=%5CRightarrow%5Ctext%20%7B%201%2C000%2C000%20%7D%20%5Ctimes%20%5Cfrac%7B%5Ctext%20%7B%20CPI%20of%20target%20year%20%7D%7D%7B%5Ctext%20%7B%20CPI%20of%20base%20year%20%7D%7D)
![\Rightarrow \frac{244}{136.2}\times1,000,000](https://tex.z-dn.net/?f=%5CRightarrow%20%5Cfrac%7B244%7D%7B136.2%7D%5Ctimes1%2C000%2C000)
![\Rightarrow 1.791483\times1,000,000](https://tex.z-dn.net/?f=%5CRightarrow%201.791483%5Ctimes1%2C000%2C000)
![\Rightarrow 1,791,483.11 \approx 1,791,483](https://tex.z-dn.net/?f=%5CRightarrow%201%2C791%2C483.11%20%5Capprox%201%2C791%2C483)
<u>Result:</u>
In 2017, The Barenaked Ladies need
to have the same amount of real purchasing power that they did in 1991.
Answer: Sky's effective interest rate on this loan is 8.39%.
In this question, we assume that interest is compounded annually.
Since Sky issues a non-interest bearing note, Star Finance will deduct 7 months' interest at 8% on the Face Value of the loan and pay the rest as principal to Sky.
Face value of the note $16 million
Discount Rate p.a 8%
Tenure of the note 7 months
![Discount on Note = Face Value * Discount Rate * \frac{Tenure in months}{Months in a year}](https://tex.z-dn.net/?f=Discount%20on%20Note%20%3D%20Face%20Value%20%2A%20Discount%20Rate%20%2A%20%5Cfrac%7BTenure%20in%20months%7D%7BMonths%20in%20a%20year%7D)
![Discount on Note = 16 * 0.08 * \frac{7}{12}](https://tex.z-dn.net/?f=Discount%20on%20Note%20%3D%2016%20%2A%200.08%20%2A%20%5Cfrac%7B7%7D%7B12%7D)
![Discount on Note = 0.746666667million](https://tex.z-dn.net/?f=Discount%20on%20Note%20%3D%200.746666667million)
[tex]Loan Amount received by Sky = Face Value - Discount on note[/tex]
![Loan Amount received by Sky = 16 - 0.746666667](https://tex.z-dn.net/?f=Loan%20Amount%20received%20by%20Sky%20%3D%2016%20-%200.746666667)
![Loan Amount received by Sky = 15.25333333 million](https://tex.z-dn.net/?f=Loan%20Amount%20received%20by%20Sky%20%3D%2015.25333333%20million)
So, Sky pays an interest of 0.746666667 on a sum of 15.25333333 for 7 months. This works out to a seven month interest of:
![Seven month Interest Rate = \frac{Interest}{Loan amount}](https://tex.z-dn.net/?f=Seven%20month%20Interest%20Rate%20%3D%20%5Cfrac%7BInterest%7D%7BLoan%20amount%7D)
![Seven month Interest Rate = \frac{0.746666667}{15.25333333}](https://tex.z-dn.net/?f=Seven%20month%20Interest%20Rate%20%3D%20%5Cfrac%7B0.746666667%7D%7B15.25333333%7D)
![Seven month Interest Rate = 0.048951049](https://tex.z-dn.net/?f=Seven%20month%20Interest%20Rate%20%3D%200.048951049)
From this we can work out the effective interest rate for Sky as follows:
![Sky's Effective Interest Rate = Seven month interest rate * \frac{12}{7}](https://tex.z-dn.net/?f=Sky%27s%20Effective%20Interest%20Rate%20%3D%20Seven%20month%20interest%20rate%20%2A%20%5Cfrac%7B12%7D%7B7%7D)
![Sky's Effective Interest Rate = 0.048951049* \frac{12}{7}](https://tex.z-dn.net/?f=Sky%27s%20Effective%20Interest%20Rate%20%3D%200.048951049%2A%20%5Cfrac%7B12%7D%7B7%7D)
![Sky's Effective Interest Rate = 0.083916084](https://tex.z-dn.net/?f=Sky%27s%20Effective%20Interest%20Rate%20%3D%200.083916084)
Answer:
Breaking through the stress in the room
I would go with C. Approach the Federal Trade Commission