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Make Three Solved Problems Each Using:

1. Simple Interest

2. Compound Interest

3. Credit Cards

4. Consumer Loans

5. Stocks

6. Bonds

7. Mutual Funds

8. Treasury Bills

 

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Sure, here are three solved problems each for the eight topics you mentioned:

1. Simple Interest:
Problem 1: John borrowed $500 from a friend and promised to pay back the money with 8% annual interest after 6 months. How much interest will John have to pay his friend when he returns the money?
Solution: Since John promised to pay back the money with simple interest, we can use the formula I = PRT, where I is the interest, P is the principal, R is the annual interest rate, and T is the time in years. Since the interest is for 6 months, we need to divide the time by 12 to get the time in years. So, I = 500 x 0.08 x (6/12) = $20. Therefore, John will have to pay $20 as interest to his friend.

Problem 2: Sarah deposited $10,000 in a bank that offered a simple interest rate of 6% per annum. After 3 years, how much interest did she earn?
Solution: Using the same formula as above, we have I = PRT = 10,000 x 0.06 x 3 = $1,800. Therefore, Sarah earned $1,800 as interest on her deposit.

Problem 3: A car dealer offers a simple interest rate of 4% per annum on a car loan of $20,000. If the loan is repaid in 5 years, how much will the borrower have to pay in total?
Solution: Again, using the formula I = PRT, we have I = 20,000 x 0.04 x 5 = $4,000 as the total interest payable. So, the borrower will have to repay the principal plus interest, which is $20,000 + $4,000 = $24,000.

2. Compound Interest:
Problem 1: Tom invested $5,000 in a fixed deposit account that earns an interest rate of 7% per annum compounded annually. How much will his investment be worth after 5 years?
Solution: Using the formula A = P(1 + r/n)^(nt), where A is the final amount, P is the principal, r is the annual interest rate, n is the number of times the interest is compounded in a year, and t is the time in years, we have A = 5,000 (1 + 0.07/1)^(1x5) = $7,246.94. Therefore, Tom's investment will be worth $7,246.94 after 5 years.

Problem 2: A credit union offers a savings account with a 5% annual interest rate compounded quarterly. If you deposit $1,000 at the beginning of each quarter for 2 years, how much will you have in the account at the end of 2 years?
Solution: Using the same formula as above, we have A = 1,000 (1 + 0.05/4)^(4x2) x 8 = $8,443.80. Therefore, you will have $8,443.80 in the account at the end of 2 years.

Problem 3: A bond with a face value of $10,000 is issued at a coupon rate of 8% per annum compounded semi-annually for 5 years. What is the total amount of interest ρáíd over the life of the bond?
Solution: Again, using the same formula as above, we have A = 10,000 (1 + 0.08/2)^(2x5) = $14,693.28. Therefore, the total interest ρáíd over the life of the bond is $14,693.28 - $10,000 = $4,693.28.

3. Credit Cards:
Problem 1: Maria has a credit card with an outstanding balance of $5,000 and an interest rate of 18% per annum. If she makes a minimum payment of $150 per month, how long will it take her to pay off the balance and what will be the total interest ρáíd?
Solution: Using the formula for the number of periods to pay off a loan, which is N = -log(1 - (R x B) / P) / log(1 + R), where N is the number of periods, R is the interest rate per period, B is the balance, and P is the payment per period, we have N = -log(1 - (0.18/12) x 5,000 / 150) / log(1 + 0.18/12) = 46.08 months, or about 4 years. The total interest ρáíd will be $3,681.55.

Problem 2: Mark has a credit card with a balance of $2,500 and an interest rate of 24% per annum. If he wants to pay off the balance in 12 months, what should his monthly payment be?
Solution: Using the same formula as above, we have P = (R x B) / (1 - (1 + R)^(-N)) = (0.24/12 x 2,500) / (1 - (1 + 0.24/12)^(-12)) = $236.99. Therefore, Mark's monthly payment should be $236.99.

Problem 3: Jill has a credit card with a balance of $3,000 and an interest rate of 20% per annum. She wants to pay off the balance in 24 months. If she makes a monthly payment of $150, how much interest will she pay in total?
Solution: Using the same formula as above, we have N = -log(1 - (0.20/12) x 3,000 / 150) / log(1 + 0.20/12) = 22.06 months, or about 2 years. Since Jill wants to pay off the balance in 24 months, she needs to increase her monthly payment. If she increases her monthly payment to $162.05, she will be able to pay off the balance in 24 months. The total interest ρáíd will be $663.27.

4. Consumer Loans:
Problem 1: Mike wants to buy a car that costs $20,000. He can either take a loan with an interest rate of 6% per annum for 5 years or pay cash. If he takes the loan, how much interest will he pay in total?
Solution: Using the formula for the total amount payable on a loan, which is A = P(1 + r/n)^(nt), where A is the total amount payable, P is the principal, r is the annual interest rate, n is the number of times the interest is compounded in a year, and t is the time in years, we have A = 20,000 (1 + 0.06/12)^(12x5) = $23,720.63. Therefore, Mike will pay $3,720.63 in interest.

Problem 2: A furniture store offers a 0% interest rate on a sofa that costs $1,000 if you pay in 12 monthly installments of $83.33 each. If you take this offer, how much will you save compared to paying cash?
Solution: If you pay cash, you will have to pay $1,000. However, if you take the offer, you will pay $83.33 x 12 = $999.96 in total. Therefore, you will save $0.04 by taking the offer.

Problem 3: Maria wants to buy a laptop that costs $1,500. She can either pay cash or take a loan with an interest rate of 10% per annum for 2 years. If she takes the loan, what will be her monthly payment and how much interest will she pay in total?
Solution: Using the same formula as above, we have A = 1,500 (1 + 0.10/12)^(12x2) = $1,783.27. Therefore, Maria will have to pay $1,783.27 in total, which is $1,783.27 - $1,500 = $283.27 in interest. Her monthly payment will be $74.30.

5. Stocks:
Problem 1: John bought 100 shares of XYZ Corporation at $50 per share and sold them at $65 per share after 2 years. What is his total gain or loss and what is his annual rate of return?
Solution: John's total gain is (65 - 50) x 100 = $1,500. His annual rate of return is [(65/50)^(1/2) - 1] x 100% = 13.39%.

Problem 2: Sarah bought 200 shares of ABC Corporation at $25 per share and sold them at $30 per share after 3 years. If she ρáíd a commission of $50 to her broker for each transaction, what is her total gain or loss?
Solution: Sarah's total cost for buying the shares was 200 x $25 = $5,000. Her total cost for selling the shares was 200 x $30 = $6,000. She ρáíd $50 x 2 = $100 in commission. Therefore, her total gain is $6,000 - $5,000 - $100 = $900.

Problem 3: Mike invested $10,000 in a mutual fund that earned an annual rate of return of 8% for 5 years. What is the total value of his investment after 5 years?
Solution: Using the formula for compound interest, we have A = P(1 + r/n)^(nt), where A is the final amount, P is the principal, r is the annual interest rate, n is the number of times the interest is compounded in a year, and t is the time in years. Therefore, A = 10,000 (1 + 0.08/1)^(1x5) = $14,693.28.

6. Bonds:
Problem 1: Jill bought a bond with a face value of $10,000 and a coupon rate of 6% per annum. If the bond matures in 5 years, what is the total amount of interest she will earn over the life of the bond?
Solution: Jill will earn $10,000 x 0.06 x 5 = $3,000 in interest over the life of the bond.

Problem 2: Tom bought a bond with a face value of $5,000 and a coupon rate of 8% per annum. If the bond matures in 3 years and he sells it after 2 years when the interest rate has fallen to 6% per annum, what is his total gain or loss?
Solution: Using the formula for the present value of a bond, which is PV = C/(1 + r)^t + F/(1 + r)^t, where PV is the present value, C is the coupon payment, F is the face value, r is the interest rate, and t is the time, we have PV = 400/(1 + 0.06)^2 + 5,000/(1 + 0.06)^3 = $4,663.79. Tom's total gain is $5,000 - $4,663.79 = $336.21.

Problem 3: Mark bought a bond with a face value of $20,000 and a coupon rate of 4% per annum. If the bond matures in 10 years and he sells it after 7 years when the interest rate has risen to 6% per annum, what is his total gain or loss?
Solution: Using the same formula as above, we have PV = 800/(1 + 0.04)^7 + 20,000/(1 + 0.04)^10 = $18,764.35. Mark's total loss is $18,764.35 - $20,000 = -$1,235.65.

7. Mutual Funds:
Problem 1: Sarah invested $5,000 in a mutual fund that earned an annual rate of return of 10% for 3 years. How much will her investment be worth after 3 years?
Solution: Using the formula for compound interest, we have A = P(1 + r/n)^(nt), where A is the final amount, P is the principal, r is the annual interest rate, n is the number of times the interest is compounded in a year, and t is the time in years. Therefore, A = 5,000 (1 + 0.10/1)^(1x3) = $6,655.10.

Problem 2: Mike invested $10,000 in a mutual fund that charged an expense ratio of 1.5% per annum. If the fund earned a rate of return of 8% per annum for 5 years, what is the total value of his investment after 5 years?
Solution: Using the formula for compound interest, we have A = P(1 + r/n)^(nt), where A is the final amount, P is the principal, r is the annual interest rate, n is the number of times the interest is compounded in a year, and t is the time in years. Therefore, A = 10,000 (1 + (0.08 - 0.015)/1)^(1x5) = $14,514.45.

Problem 3: Jill invested $2,000 in a mutual fund that charged a front-end load of 5%. If the fund earned a rate of return of 12% per annum for 2 years, what is the total value of her investment after 2 years?
Solution: Using the formula for compound interest and factoring in the front-end load, we have A = (1 - 0.05) x 2,000 x (1 + 0.12/1)^(1x2) = $2,730.40.

8. Treasury Bills:
Problem 1: John bought a 1-year Treasury bill with a face value of $10,000 for $9,500. What is his annual rate of return?
Solution: John's annual rate of return is (10,000 - 9,500) / 9,500 x 100% = 5.26%.

Problem 2: Sarah bought a 6-month Treasury bill with a face value of $5,000 for $4,800. What is her annual rate of return?
Solution: Sarah's annual rate of return is (5,000 - 4,800) / 4,800 x 200% = 16.67%.

Problem 3: Mike bought a 3-month Treasury bill with a face value of $2,000 for $1,950. What is his annual rate of return?
Solution: Mike's annual rate of return is (2,000 - 1,950) / 1,950 x 400% = 10.26%.