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Sure, here are three solved problems for each of the given topics:
1. Simple Interest:
Problem 1: Tom deposited $5,000 in a savings account that pays 3% simple interest per year. How much interest will he earn after 2 years?
Solution:
Simple interest = (P x R x T)/100
= (5000 x 3 x 2)/100
= $300
Therefore, Tom will earn $300 in interest after 2 years.
Problem 2: Cathy borrowed $10,000 from a friend at a simple interest rate of 4.5% per year for 3 years. How much interest will she pay her friend at the end of the loan period?
Solution:
Simple interest = (P x R x T)/100
= (10000 x 4.5 x 3)/100
= $1350
Therefore, Cathy will pay $1350 in interest at the end of the 3-year loan period.
Problem 3: John borrowed $2,500 from a bank at a simple interest rate of 2.5% per year. He repaid the loan after 1 year. How much did he have to pay back in total?
Solution:
Simple interest = (P x R x T)/100
= (2500 x 2.5 x 1)/100
= $62.50
Total amount to be ρáíd back = Principal + Interest
= 2500 + 62.50
= $2,562.50
2. Compound Interest:
Problem 1: Mark invested $10,000 in a savings account that pays 4% compound interest per year. How much will he have at the end of 5 years?
Solution:
Future value = P (1 + r/n)^(n x T)
= 10000 (1 + 0.04/12)^(12 x 5)
= $12,167.26
Therefore, Mark will have $12,167.26 at the end of 5 years.
Problem 2: Sarah took a loan of $15,000 from a bank that charges 5% compound interest per year. She wants to repay the loan in 3 years. How much will she have to pay back in total?
Solution:
Future value = P (1 + r/n)^(n x T)
= 15000 (1 + 0.05/12)^(12 x 3)
= $17,228.27
Therefore, Sarah will have to pay back $17,228.27 in total.
Problem 3: David invested $8,000 in a mutual fund that earns a compound interest rate of 6% per year. How much will he have at the end of 10 years?
Solution:
Future value = P (1 + r/n)^(n x T)
= 8000 (1 + 0.06/1)^(1 x 10)
= $18,194.72
Therefore, David will have $18,194.72 at the end of 10 years.
3. Credit Cards:
Problem 1: Lisa has a credit card with a balance of $2,000 and an interest rate of 18% per annum. She makes a payment of $100 every month. How long will it take for her to pay off the balance?
Solution:
Using the formula: Number of periods = - (log(1 - (r x PV) / PMT)) / log(1 + r)
where PV is the present value, PMT is the payment, and r is the monthly interest rate.
r = 0.18/12 = 0.015
PV = 2000
PMT = 100
Number of periods = - (log(1 - (0.015 x 2000) / 100)) / log(1 + 0.015)
= 20.22
Therefore, it will take Lisa approximately 21 months (20.22 rounded up) to pay off the balance.
Problem 2: Jack has three credit cards with balances of $2,500, $3,000, and $1,500, with interest rates of 20%, 18%, and 22% per annum, respectively. He wants to pay off all the cards in 2 years. How much does he need to pay each month?
Solution:
Total balance = $2,500 + $3,000 + $1,500 = $7,000
Total interest rate = (2500 x 0.20) + (3000 x 0.18) + (1500 x 0.22) = $1,870
Total amount to be ρáíd in 2 years = $7,000 + $1,870 = $8,870
Monthly payment = Total amount to be ρáíd / Number of months
= 8870 / 24
= $369.58
Therefore, Jack needs to pay $369.58 per month to pay off all the credit cards in 2 years.
Problem 3: Rachel has a credit card balance of $4,000 with an interest rate of 15% per annum. She is making minimum payments of $80 each month. How long will it take for her to pay off the balance?
Solution:
Using the formula: Number of periods = - (log(1 - (r x PV) / PMT)) / log(1 + r)
where PV is the present value, PMT is the payment, and r is the monthly interest rate.
r = 0.15/12 = 0.0125
PV = 4000
PMT = 80
Number of periods = - (log(1 - (0.0125 x 4000) / 80)) / log(1 + 0.0125)
= 94.55
Therefore, it will take Rachel approximately 95 months (94.55 rounded up) to pay off the balance.
4. Consumer Loans:
Problem 1: Sarah took out a $10,000 loan to buy a car at an annual interest rate of 5%. The loan is to be repaid in 3 years. What will be the monthly payments?
Solution:
Using the formula: Monthly payment = (P x r x (1 + r)^n) / ((1 + r)^n - 1)
where P is the principal, r is the monthly interest rate, and n is the number of months.
r = 0.05/12 = 0.00417
n = 3 x 12 = 36
Monthly payment = (10000 x 0.00417 x (1 + 0.00417)^36) / ((1 + 0.00417)^36 - 1)
= $295.24
Therefore, the monthly payments will be $295.24.
Problem 2: John took out a loan of $20,000 to renovate his house at an annual interest rate of 6%. The loan is to be repaid in 5 years. What will be the total amount he has to pay back?
Solution:
Using the formula: Total amount to be ρáíd = Monthly payment x Number of months
where Monthly payment is calculated using the formula given in problem 1, and Number of months = 5 x 12 = 60.
Monthly payment = $386.66 (calculated using the formula in problem 1)
Total amount to be ρáíd = $386.66 x 60 = $23,199.60
Therefore, John has to pay back a total amount of $23,199.60.
Problem 3: Mary took out a loan of $5,000 to pay for her wedding expenses at an annual interest rate of 8%. The loan is to be repaid in 2 years. What will be the total interest ρáíd?
Solution:
Using the formula: Total interest ρáíd = (P x r x n) - P
where P is the principal, r is the monthly interest rate, and n is the number of months.
r = 0.08/12 = 0.00667
n = 2 x 12 = 24
Total interest ρáíd = (5000 x 0.00667 x 24) - 5000
= $800
Therefore, Mary will pay a total interest of $800.
5. Stocks:
Problem 1: Susan bought 200 shares of XYZ company at $50 per share. She sold the shares after 1 year at $60 per share. What is her profit?
Solution:
Profit = (Selling price - Cost price) x Number of shares
= ($60 - $50) x 200
= $2,000
Therefore, Susan's profit is $2,000.
Problem 2: John invested $5,000 in ABC company which pays a dividend of $2 per share. If the current market price of the stock is $40, what is his dividend yield?
Solution:
Dividend yield = (Dividend per share / Cost per share) x 100%
= ($2 / $40) x 100%
= 5%
Therefore, John's dividend yield is 5%.
Problem 3: Lisa purchased 100 shares of XYZ company at $70 per share. After 6 months, the stock price went up to $80 per share, and she sold the shares. What is her return on investment?
Solution:
Return on investment = (Total earnings / Cost of investment) x 100%
Total earnings = (Selling price - Buying price) x Number of shares
= ($80 - $70) x 100
= $1,000
Cost of investment = Buying price x Number of shares
= $70 x 100
= $7,000
Return on investment = ($1,000 / $7,000) x 100%
= 14.29%
Therefore, Lisa's return on investment is 14.29%.
6. Bonds:
Problem 1: ABC company issued a bond with a face value of $10,000, a coupon rate of 8%, and a maturity period of 5 years. What will be the total interest ρáíd by the company?
Solution:
Total interest ρáíd = (Face value x Coupon rate x Time period) / 100
= (10000 x 8 x 5) / 100
= $4,000
Therefore, the total interest ρáíd by the company will be $4,000.
Problem 2: XYZ company issued a bond with a face value of $25,000, a coupon rate of 6%, and a maturity period of 10 years. If the current market interest rate is 8%, what will be the bond's price?
Solution:
Using the formula: Bond price = (Coupon payment / Interest rate) x (1 - 1 / (1 + Interest rate)^Time period) + (Face value / (1 + Interest rate)^Time period)
where Coupon payment = Face value x Coupon rate, Interest rate = market interest rate, and Time period = maturity period.
Coupon payment = 25000 x 0.06 = $1,500
Interest rate = 0.08
Time period = 10
Bond price = (1500 / 0.08) x (1 - 1 / (1 + 0.08)^10) + (25000 / (1 + 0.08)^10)
= $17,794.41
Therefore, the bond's price is $17,794.41.
Problem 3: PQR company issued a bond with a face value of $50,000, a coupon rate of 7%, and a maturity period of 15 years. If the bond is currently selling at $60,000, what is its yield to maturity?
Solution:
Using trial and error method, we can calculate that the yield to maturity is 5.86% (rounded to two decimal places).
Therefore, the bond's yield to maturity is 5.86%.
7. Mutual Funds:
Problem 1: John invested $10,000 in a mutual fund with a NAV of $50 per share. He bought 200 shares. What will be his return on investment if the NAV increased to $60 per share after 1 year?
Solution:
Return on investment = ((Selling price - Buying price) x Number of shares) / Buying price
= (($60 - $50) x 200) / ($50 x 200)
= 20%
Therefore, John's return on investment is 20%.
Problem 2: Sarah invested $5,000 in a mutual fund that charges a front-end load of 3%. If the NAV is $25 per share, how many shares will she be able to purchase?
Solution:
Total cost of investment = Amount invested x (1 - Front-end load)
= $5,000 x (1 - 0.03)
= $4,850
Number of shares purchased = Total cost of investment / NAV
= $4,850 / $25
= 194
Therefore, Sarah will be able to purchase 194 shares.
Problem 3: Lisa invested $2,500 in a mutual fund which has an expense ratio of 1.5%. If the NAV is $20 per share, how many shares will she be able to purchase?
Solution:
Total cost of investment = Amount invested x (1 - Expense ratio)
= $2,500 x (1 - 0.015)
= $2,462.50
Number of shares purchased = Total cost of investment / NAV
= $2,462.50 / $20
= 123.13 (rounded down)
Therefore, Lisa will be able to purchase 123 shares.
8. Treasury Bills:
Problem 1: Susan bought a 3-month Treasury bill with a face value of $10,000 at a discount rate of 4%. What will be the yield on the bill?
Solution:
Yield on the bill = (Face value - Purchase price) / Face value x (360 / Time period)
= (10000 - 9960) / 10000 x (360 / 3)
= 4.8%
Therefore, the yield on the bill is 4.8%.
Problem 2: John bought a 6-month Treasury bill with a face value of $20,000 at a discount rate of 3.5%. What will be the purchase price?
Solution:
Purchase price = Face value x (1 - Discount rate x Time period /360)
= 20000 x (1 - 0.035 x 6/360)
= $19,885
Therefore, the purchase price of the bill is $19,885.
Problem 3: Lisa bought a 1-year Treasury bill with a face value of $5,000 at a discount rate of 4.5%. What will be the yield to maturity?
Solution:
Using the formula: Yield to maturity = ((Face value / Purchase price)^(365/Time period)) - 1
= ((5000 / 5248.44)^(365/365)) - 1
= 4.44%
Therefore, the yield to maturity is 4.44%.
1. Simple Interest:
Problem 1: Tom deposited $5,000 in a savings account that pays 3% simple interest per year. How much interest will he earn after 2 years?
Solution:
Simple interest = (P x R x T)/100
= (5000 x 3 x 2)/100
= $300
Therefore, Tom will earn $300 in interest after 2 years.
Problem 2: Cathy borrowed $10,000 from a friend at a simple interest rate of 4.5% per year for 3 years. How much interest will she pay her friend at the end of the loan period?
Solution:
Simple interest = (P x R x T)/100
= (10000 x 4.5 x 3)/100
= $1350
Therefore, Cathy will pay $1350 in interest at the end of the 3-year loan period.
Problem 3: John borrowed $2,500 from a bank at a simple interest rate of 2.5% per year. He repaid the loan after 1 year. How much did he have to pay back in total?
Solution:
Simple interest = (P x R x T)/100
= (2500 x 2.5 x 1)/100
= $62.50
Total amount to be ρáíd back = Principal + Interest
= 2500 + 62.50
= $2,562.50
2. Compound Interest:
Problem 1: Mark invested $10,000 in a savings account that pays 4% compound interest per year. How much will he have at the end of 5 years?
Solution:
Future value = P (1 + r/n)^(n x T)
= 10000 (1 + 0.04/12)^(12 x 5)
= $12,167.26
Therefore, Mark will have $12,167.26 at the end of 5 years.
Problem 2: Sarah took a loan of $15,000 from a bank that charges 5% compound interest per year. She wants to repay the loan in 3 years. How much will she have to pay back in total?
Solution:
Future value = P (1 + r/n)^(n x T)
= 15000 (1 + 0.05/12)^(12 x 3)
= $17,228.27
Therefore, Sarah will have to pay back $17,228.27 in total.
Problem 3: David invested $8,000 in a mutual fund that earns a compound interest rate of 6% per year. How much will he have at the end of 10 years?
Solution:
Future value = P (1 + r/n)^(n x T)
= 8000 (1 + 0.06/1)^(1 x 10)
= $18,194.72
Therefore, David will have $18,194.72 at the end of 10 years.
3. Credit Cards:
Problem 1: Lisa has a credit card with a balance of $2,000 and an interest rate of 18% per annum. She makes a payment of $100 every month. How long will it take for her to pay off the balance?
Solution:
Using the formula: Number of periods = - (log(1 - (r x PV) / PMT)) / log(1 + r)
where PV is the present value, PMT is the payment, and r is the monthly interest rate.
r = 0.18/12 = 0.015
PV = 2000
PMT = 100
Number of periods = - (log(1 - (0.015 x 2000) / 100)) / log(1 + 0.015)
= 20.22
Therefore, it will take Lisa approximately 21 months (20.22 rounded up) to pay off the balance.
Problem 2: Jack has three credit cards with balances of $2,500, $3,000, and $1,500, with interest rates of 20%, 18%, and 22% per annum, respectively. He wants to pay off all the cards in 2 years. How much does he need to pay each month?
Solution:
Total balance = $2,500 + $3,000 + $1,500 = $7,000
Total interest rate = (2500 x 0.20) + (3000 x 0.18) + (1500 x 0.22) = $1,870
Total amount to be ρáíd in 2 years = $7,000 + $1,870 = $8,870
Monthly payment = Total amount to be ρáíd / Number of months
= 8870 / 24
= $369.58
Therefore, Jack needs to pay $369.58 per month to pay off all the credit cards in 2 years.
Problem 3: Rachel has a credit card balance of $4,000 with an interest rate of 15% per annum. She is making minimum payments of $80 each month. How long will it take for her to pay off the balance?
Solution:
Using the formula: Number of periods = - (log(1 - (r x PV) / PMT)) / log(1 + r)
where PV is the present value, PMT is the payment, and r is the monthly interest rate.
r = 0.15/12 = 0.0125
PV = 4000
PMT = 80
Number of periods = - (log(1 - (0.0125 x 4000) / 80)) / log(1 + 0.0125)
= 94.55
Therefore, it will take Rachel approximately 95 months (94.55 rounded up) to pay off the balance.
4. Consumer Loans:
Problem 1: Sarah took out a $10,000 loan to buy a car at an annual interest rate of 5%. The loan is to be repaid in 3 years. What will be the monthly payments?
Solution:
Using the formula: Monthly payment = (P x r x (1 + r)^n) / ((1 + r)^n - 1)
where P is the principal, r is the monthly interest rate, and n is the number of months.
r = 0.05/12 = 0.00417
n = 3 x 12 = 36
Monthly payment = (10000 x 0.00417 x (1 + 0.00417)^36) / ((1 + 0.00417)^36 - 1)
= $295.24
Therefore, the monthly payments will be $295.24.
Problem 2: John took out a loan of $20,000 to renovate his house at an annual interest rate of 6%. The loan is to be repaid in 5 years. What will be the total amount he has to pay back?
Solution:
Using the formula: Total amount to be ρáíd = Monthly payment x Number of months
where Monthly payment is calculated using the formula given in problem 1, and Number of months = 5 x 12 = 60.
Monthly payment = $386.66 (calculated using the formula in problem 1)
Total amount to be ρáíd = $386.66 x 60 = $23,199.60
Therefore, John has to pay back a total amount of $23,199.60.
Problem 3: Mary took out a loan of $5,000 to pay for her wedding expenses at an annual interest rate of 8%. The loan is to be repaid in 2 years. What will be the total interest ρáíd?
Solution:
Using the formula: Total interest ρáíd = (P x r x n) - P
where P is the principal, r is the monthly interest rate, and n is the number of months.
r = 0.08/12 = 0.00667
n = 2 x 12 = 24
Total interest ρáíd = (5000 x 0.00667 x 24) - 5000
= $800
Therefore, Mary will pay a total interest of $800.
5. Stocks:
Problem 1: Susan bought 200 shares of XYZ company at $50 per share. She sold the shares after 1 year at $60 per share. What is her profit?
Solution:
Profit = (Selling price - Cost price) x Number of shares
= ($60 - $50) x 200
= $2,000
Therefore, Susan's profit is $2,000.
Problem 2: John invested $5,000 in ABC company which pays a dividend of $2 per share. If the current market price of the stock is $40, what is his dividend yield?
Solution:
Dividend yield = (Dividend per share / Cost per share) x 100%
= ($2 / $40) x 100%
= 5%
Therefore, John's dividend yield is 5%.
Problem 3: Lisa purchased 100 shares of XYZ company at $70 per share. After 6 months, the stock price went up to $80 per share, and she sold the shares. What is her return on investment?
Solution:
Return on investment = (Total earnings / Cost of investment) x 100%
Total earnings = (Selling price - Buying price) x Number of shares
= ($80 - $70) x 100
= $1,000
Cost of investment = Buying price x Number of shares
= $70 x 100
= $7,000
Return on investment = ($1,000 / $7,000) x 100%
= 14.29%
Therefore, Lisa's return on investment is 14.29%.
6. Bonds:
Problem 1: ABC company issued a bond with a face value of $10,000, a coupon rate of 8%, and a maturity period of 5 years. What will be the total interest ρáíd by the company?
Solution:
Total interest ρáíd = (Face value x Coupon rate x Time period) / 100
= (10000 x 8 x 5) / 100
= $4,000
Therefore, the total interest ρáíd by the company will be $4,000.
Problem 2: XYZ company issued a bond with a face value of $25,000, a coupon rate of 6%, and a maturity period of 10 years. If the current market interest rate is 8%, what will be the bond's price?
Solution:
Using the formula: Bond price = (Coupon payment / Interest rate) x (1 - 1 / (1 + Interest rate)^Time period) + (Face value / (1 + Interest rate)^Time period)
where Coupon payment = Face value x Coupon rate, Interest rate = market interest rate, and Time period = maturity period.
Coupon payment = 25000 x 0.06 = $1,500
Interest rate = 0.08
Time period = 10
Bond price = (1500 / 0.08) x (1 - 1 / (1 + 0.08)^10) + (25000 / (1 + 0.08)^10)
= $17,794.41
Therefore, the bond's price is $17,794.41.
Problem 3: PQR company issued a bond with a face value of $50,000, a coupon rate of 7%, and a maturity period of 15 years. If the bond is currently selling at $60,000, what is its yield to maturity?
Solution:
Using trial and error method, we can calculate that the yield to maturity is 5.86% (rounded to two decimal places).
Therefore, the bond's yield to maturity is 5.86%.
7. Mutual Funds:
Problem 1: John invested $10,000 in a mutual fund with a NAV of $50 per share. He bought 200 shares. What will be his return on investment if the NAV increased to $60 per share after 1 year?
Solution:
Return on investment = ((Selling price - Buying price) x Number of shares) / Buying price
= (($60 - $50) x 200) / ($50 x 200)
= 20%
Therefore, John's return on investment is 20%.
Problem 2: Sarah invested $5,000 in a mutual fund that charges a front-end load of 3%. If the NAV is $25 per share, how many shares will she be able to purchase?
Solution:
Total cost of investment = Amount invested x (1 - Front-end load)
= $5,000 x (1 - 0.03)
= $4,850
Number of shares purchased = Total cost of investment / NAV
= $4,850 / $25
= 194
Therefore, Sarah will be able to purchase 194 shares.
Problem 3: Lisa invested $2,500 in a mutual fund which has an expense ratio of 1.5%. If the NAV is $20 per share, how many shares will she be able to purchase?
Solution:
Total cost of investment = Amount invested x (1 - Expense ratio)
= $2,500 x (1 - 0.015)
= $2,462.50
Number of shares purchased = Total cost of investment / NAV
= $2,462.50 / $20
= 123.13 (rounded down)
Therefore, Lisa will be able to purchase 123 shares.
8. Treasury Bills:
Problem 1: Susan bought a 3-month Treasury bill with a face value of $10,000 at a discount rate of 4%. What will be the yield on the bill?
Solution:
Yield on the bill = (Face value - Purchase price) / Face value x (360 / Time period)
= (10000 - 9960) / 10000 x (360 / 3)
= 4.8%
Therefore, the yield on the bill is 4.8%.
Problem 2: John bought a 6-month Treasury bill with a face value of $20,000 at a discount rate of 3.5%. What will be the purchase price?
Solution:
Purchase price = Face value x (1 - Discount rate x Time period /360)
= 20000 x (1 - 0.035 x 6/360)
= $19,885
Therefore, the purchase price of the bill is $19,885.
Problem 3: Lisa bought a 1-year Treasury bill with a face value of $5,000 at a discount rate of 4.5%. What will be the yield to maturity?
Solution:
Using the formula: Yield to maturity = ((Face value / Purchase price)^(365/Time period)) - 1
= ((5000 / 5248.44)^(365/365)) - 1
= 4.44%
Therefore, the yield to maturity is 4.44%.
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