Westminster International University in Tashkent buss001c quantitative Methods, Semester I, 2021/2022 Seminar Percentage and Interest rates

Westminster International University in Tashkent
3BUSS001C - Quantitative Methods, Semester I, 2021/2022


Seminar 5 Percentage and Interest rates
1. Convert each of the following fractions to percentage:

1. 
   3/25 =
   
2. 
   4/5 =
   
3. 
   3/4 =
   
4. 
   2/3 =
   
5. 
   1 =
   

2. Calculate a percentage of a given quantity.
a. Find 40 % of 240
b. Find 10 % of 1 hour
c. Find 15 % of $250.
d. Find 120 % of 25 km


3. Increase or decrease a quantity by a given percentage.
a. The price of rice is increased from $10 to $12.50 per kg. Find the percentage increase in price.
b. The population in a small town increases from 20,000 to 21,250 in one year. Find the percentage increase in population.
c. The cost of an article is decreased by 15%. If the original cost is $80, find the decrease cost.
d. A television manufacturing company declares that a television is now available for $5600 as against $8400 one year before. Find the percentage reduction in the price of television offered by the company.


4. Real-life problem.
In an election, candidate A got 75% of the total valid votes. If 15% of the total votes were declared invalid and the total numbers of votes is 560000, find the number of valid votes polled in favor of candidate.


5. Interest rates (simple vs compound)

1. 
   $250 is invested at a bank that pays 7% simple interest. Calculate the amount of money in the account after 1 year, 3 years, 7 years, and 20 years.
   
2. 
   John wants to have an interest income of $3,000 a year. How much must he invest for one year at 8%?
   
3. 
   Jane owes the bank some money at 4% per year. After half a year, she paid $45 as interest. How much money does she owe the bank?
   
4. 
   1mln soums is invested at a bank that pays 20% compound interest, compounded annually. Calculate the amount of money in the account after 4 years, (Homework: 7 years, and 20 years).
   
5. 
   1mln soums is invested at a bank that pays 20% compound interest, compounded semi-annually. Calculate the amount of money in the account after 4 years, (Homework: 7 years, and 20 years).
   

6. Perpetuity

1. 
   Your broker has offered you an investment vehicle which will pay you (or your descendants) $36,000 per year forever with the first payment coming one year from today. If the interest rate is 4%, how much is the investment vehicle worth to you today?
   
2. 
   Currently you have $200,000 to invest in a project that pays perpetually 12% of your investment. How much money will it pay every year?
   
3. 
   A local bank will pay you $500 a year for your lifetime if you deposit $10,000 in the bank today. If you plan to live forever, what interest rate is the bank paying?
   
4. 
   Using the rule of 72, if the interest rate is 12%, how l;ong will it take for you to double your money?
   

7. Nominal vs Real interest rate
Your local bank is offering 15% annual interest rate on deposit. The inflation rate is 5.5%. Calculate the exact real interest rate using the formula.
8. Effective annual interest rate and Annual Percentage Rate (APR)
a. If an eight-year interest-bearing account yields a 20 percent nominal annual rate of return that is compounded semi-annually, what is the account's effective annual rate of return?
b. First National Bank pays 6.2% interest compounded semiannually. Second National Bank pays pays 6% interest, compounded monthly. Which bank offers the higher effective annual rate?