Name: FIN 1050 Time Value of Money Problems Directions: Using Appendix A in the back of your book (Compound Sum of $1), calculate the following problems: 1. Susan s parents have invested $20,000 for her college education in a savings account earning 3% interest. How much will the savings account be worth in four years when she is ready for college? How much interest will she have earned? Future Value Calculation: Interest Earned: The intersection of n=4 and 3% is $20,000 X factor = Future Value Future value - present value $20,000 x = $ $ - $ = $ What if Susan s parents invested $30,000 instead? Factor: $ X = $ $ - $ = $ 2. Ben invested $30,000 into his 401(k), which earns 8%. What will his investment be worth in 30 years when he is ready to retire? Future Value Calculation: Interest Earned: What if he waits 40 years to retire? What will his investment be worth then? Factor: $ X = $ $ - $ = $ 3. Brian earned $500 last summer from mowing lawns. He wants to invest his money for 5 years into a CD earning 5%. How much will his CD be worth at the end of 5 years? Future Value Calculation: Interest Earned: What if Brian leaves his CD for 8 years? What will it be worth then? Factor: $ X = $ $ - $ = $ 1 P age
4. Cheri invested in a $1,500 CD earning 3%. What will the CD be worth in three years? Future Value Calculation: Interest Earned: What if Cheri invested $3,000 instead? What will it be worth after three years? Factor: $ X = $ $ - $ = $ 5. Jen invested $12,000 into her retirement account that earns 11%. What will her retirement account be worth in 20 years? Future Value Calculation: Interest Earned: What will the retirement account be worth in 40 years? Factor: $ X = $ $ - $ = $ Directions: Using Appendix B in the back of your book (Present Value of $1), calculate the following problems: 6. Josh needs $15,000 for college tuition four years from now. If he could get 8% interest, how much would he need to invest today in order to reach his goal? Present Value Calculation: Interest Earned: The intersection of n=4 and 8% is $15,000 X factor = Present Value Future value - present value $15,000 x = $ $ - $ = $ What if he could take 6 years to reach his goal instead? How much would he have to save today? Factor: $ - $ = $ 7. Kristin anticipates that she will need $500,000 to finance her retirement in 40 years. If she could earn 10%, how much would she need to invest today to reach her goal? Present Value Calculation: Interest Earned: $ - $ = $ What if she waited 50 years to take the money out? What would she need to invest today? Factor: $ - $ = $ 2 P age
8. Weddings are expensive! You think you will need to have $12,000 and plan on getting married in 8 years. If you could get 4% in your savings account, how much would you have to put away today to reach your goal in 8 years? Present Value Calculation: Interest Earned: $ - $ = $ What if you lowered your expectations and only need $9,000? How much would you have to save? Factor: $ - $ = $ 9. Your dream vacation is in Hawaii. You think you will need $5,000 for the perfect vacation, and you are going to save for three years, earning 13%. How much do you need to put aside today to reach your goal? Present Value Calculation: Interest Earned: $ - $ = $ What if the vacation is five years away instead of three? What would you need to save today? Factor: $ - $ = $ 10. Steffie would like to have $3000 in a year for a down payment on a new car. If she could get a certificate of deposit paying 5%, how much would she have to put in the CD today to reach her goal? Present Value Calculation: Interest Earned: $ - $ = $ What if she needs $5,000 instead? How much would she have to put in her CD today? Factor: $ - $ = $ Directions: Using Appendix C in the back of your book (Compound Sum of an Annuity of $ for n Periods), calculate the following problems: 11. Josh needs $15,000 for college tuition four years from now. If he could get 8% interest, how much would he need to save every year to be able to reach his goal? The intersection of n=4 and 8% is Annuity Value Calculation: $15,000 / factor = Amount to be saved each year $15,000 / = $ What if he could take 6 years to reach his goal instead? How much would he have to save today? Factor: 3 P age
12. Kristin anticipates that she will need $500,000 to finance her retirement in 40 years. If she could earn 10%, how much would she need to invest every year to reach her goal? Annuity Value Calculation: What if she waited 50 years to take the money out? What would she need to invest every year? Factor: 13. Weddings are expensive! You think you will need to have $12,000 and plan on getting married in 8 years. If you could get 4% in your savings account, how much would you have to put away every year to reach your goal in 8 years? Annuity Value Calculation: What if you lowered your expectations and only need $9,000? How much would you have to save? Factor: 14. Your dream vacation is in Hawaii. If you want to go on your vacation in three years, and you could save $1,250 a year at 13%, how much would you have at the end of three years? Ending Amount: What if the vacation is five years away instead of three? Saving at the same rate, how much would you have then? Factor: 15. Steffie would like to save money for the down payment on a new car. If she could save $750 a year for the next three years at 3%, how much would she have in three years? Ending Amount What if she could get 4% instead? What would it be worth in three years? Factor: 4 P age
Directions: Using Appendix E in the back of your book (Monthly Installment Loan Tables), calculate the following problems: Be sure to multiply the factor in the table by the amount of the loan, moving the decimal point three to the left. 16. Tammy has found her first car, a used Honda Accord. The cost is $15,000. Assuming Tammy wants to pay off the balance in four years with financing of 9%, what would her monthly payments be? Be sure to move the decimal place on the loan amount three to the left! The intersection of 9% and 48 months is: $15 X factor = Monthly Payment $15 x = $ What if she decides to pay off the loan in 60 months instead? What would the monthly payment be? Factor: $ X = $_ 17. Chloe purchased a new tablet computer for $800. She borrowed the money from her parents VISA card at an interest rate of 14.5%, and will pay it off in one year. How much does she need to pay each month? Be sure to move the decimal place on the loan amount three to the left! $ X = $_ What if the VISA rate is only 10%? How much will her monthly payment be? Factor: $ X = $_ 18. Will purchased a new motorcycle for $8,500. He received financing from his local bank at 11% interest. He would like to pay off the loan in two years. How much will his monthly payment be? Be sure to move the decimal place on the loan amount three to the left! $ X = $_ What if Will pays off the debt in three years instead? What will his monthly payment be? Factor: $ X = $_ 5 P age 19. Sara desperately wants a new dress for prom. The cost is $750. She borrows the money from her brother and agrees to pay 12% interest and pay it off in 6 months. How much will she need to pay a month? Be sure to move the decimal place on the loan amount three to the left! $ X = $_ What if Sara gets a $500 dress instead? What will her monthly payments be? Factor: $ X = $_
20. Drew decided to buy a new bike for $3,000. He was able to get financing from his parents credit union for 9.5%. The credit union wants him to pay it off in four years. How much will he pay each month? Be sure to move the decimal place on the loan amount three to the left! $ X = $_ What if Drew gets a different bike for $3,500 instead? How much will his monthly payment be? Factor: $ X = $_ PART 5: RULE OF 72 How long will it take the following investments to double? Remember to divide 72 by the interest rate to get the number of years it will take to double once. Round your answers to two decimal places. Investment Interest Rate Years to Double Money Market Mutual Fund 3.1 years Small Company Stock 12.6 years 3 year Certificate of Deposit 2.8 years 5 year Certificate of Deposit 5.1 years Large Company Stock 11.3 years Government Bond 5.3 years Treasury Bills 3.8 years Money Market Account 2.6 years Savings Account 2.3 years The Rule of 72 will also tell you how many times an investment will double over a period of time. Directions: Step 1: Using the Rule of 72, determine how long it will take your investment to double once. Step 2: Fill out the table. Add the number of years you determined in #1, over and over until the desired ending time period. Step 3: Every time you add the number of years, double the investment. Solve Rhonda s problem: Rhonda is 22 years old and would like to invest $2,500 into a U.S. Treasury Note earning 7.5% interest. How many times will Rhonda s investment double before she withdraws it at age 70? Step 1: How long will it take for her investment to double once? / = Years 6 P age
Step 2 and 3: Fill out the table below. In the first column, add the number you determined in #1 above, over and over until you reach age 70. In the second column, double the investment with every row. Age Investment Amount 22 $ $2,500 $ $ $ $ $ Here is another example: $500 invested at age 18; 7.06% interest. How many times will the investment double by age 69? (round to the nearest hundredth) Step 1: How long will it take for the investment to double once? / = years Step 2 and 3: Fill out the table below. In the first column, add the number you determined in #1 above, over and over until you reach age 70. In the second column, double the investment with every row. Age Investment Amount 18 $ $500 $ $ $ $ $ 7 P age