# Time Value of Money - Table of Contents

**TVM01 – Future Value of a Single Sum Problem – What is the future value of $60,000 invested for 6 years compounded annually at an interest rate of 8.5%?**

**TVM02 – ****Future Value of a Single Sum – Semiannual Interest – ****Assume that GE deposits $1,500,000 into the Ohio River Bank at the beginning of 2015 as a commitment toward building a new manufacturing plant to be completed December 31st, 2019. How much will the company have on deposit at the end of five years if interest is 8.5% compounded semi-annually? **

**TVM03 – Present Value of a Single Sum – ****What is the present value of $115,292 to be paid in six years discounted at 11.5% compounded annually? **

**TVM04 – Present Value of a Single Sum – ****Savings Example – Assume that your dad decides to give you $4,000 for a trip to Australia when you graduate from college four years from now. He proposes to finance a trip by investing a sum of money now at 7.5% compound interest that will provide you with the $4,000 upon your graduation. What amount must he invest today?**

**TVM05** **– Present Value of a Single Sum –****Unknown Number of Periods – ****Assume you want to accumulate $80,000 in a fund to build a new house. At the beginning of the current year, you deposit $50,000 in a fund that earns 10.5% compounded annually. How many years will it take to accumulate $80,000 in the fund?**

**TVM06 ****– Present Value of a Single Sum – ****Unknown Interest Rate – ****Your company needs $1,500,000 to build a new manufacturing plant six years from now. Your company currently has $800,000 to invest to build this plant. At what rate of interest must it invest the $800,000 to fund the plant six years from now? **

**TVM07 – Future Value of an Annuity – What is the future value of $6,000 deposits made at the end of the next six years earning interest of 8.5%?**

**TVM08 ****– Future Value of an Annuity -Semiannual Periods – ****Assume that your company deposits $80,000 at the end of each six-month period for the next four years to accumulate enough money to meet debts that mature in four years. What is the future value that your company will have on deposit at the end of four years if the annual interest rate is 9.5%?**

**TVM10 – ****This is a future value of an annuity problem in which the payment is the unknown. – ****Assume that you plan to accumulate $30,000 for a down payment on a house six years from now. For the next six years, you earn an annual return of 10%, compounded semi-annually. How much should you deposit at the end of each six-month period?**

**TVM13 – Present Value of an Annuity – What is the present value of rental receipts of $7,000 to be received at the end of each of the next 6 years when discounted at 11.5%?**

**T****VM14**** – Present Value of an Annuity – You have just won $1,000,000 in your state’s weekly lottery. You will be receiving $50,000 per year for 20 years. Assuming an interest rate of 8.5%, what is the present value of that annuity?**

**TVM09 – Future Value of an Annuity Due – In a future value of annuity due problem, the payment is made at the beginning of the year. As****sume that you plan to deposit $950 per year on each birthday of your son Richard. You make the first deposit on his tenth birthday, at 7.5% compounded annually. What amount will you have accumulated for college expenses by your son’s eighteenth birthday?**

**TVM11 – Future Value of an Annuity Due –****Retirement Problem – ****You would like to create a retirement fund. You deposit $3,000 today in a savings account that earns 6.5% interest. You plan to deposit $3,000 every year for a total of 35 years. How much cash will you accumulate in your retirement savings account when you retire in 35 years?**

**TVM12** **– ****Future Value of an Annuity, Unknown Payment – ****Suppose that a company’s goal is to accumulate $145,100 by making periodic deposits of $25,000 at the end of each year, which will earn 7.5% compounded annually while accumulating. How many deposits must it make? The $145,100 represents the future value of how many $25,000 deposits at a 7.5% annual rate of interest?**

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**TVM15 – Present Value of an Annuity Due – ****Amazon, Inc. rents a warehouse for 5 years with annual rent payments of $2.5 million made at the beginning of each year. If the interest rate is 8.6%, what is the present value of the rental obligations?**

**TVM16 (a) ****Richard wishes to become a millionaire. His investment account has a balance of $150,000 and has a guaranteed interest of 9.5%. How many years does Richard leave this balance invested in his fund to achieve his targeted $1,000,000?**

**TVM16(b) ****Assume that Marilyn wants to accumulate $1 million in 18 years using her investment fund balance of $250,000. At what interest rate must Marilyn’s investment compound annually?**

TVM17 The Campbell Company is considering either buying or leasing a manufacturing plant and is evaluating three alternatives. Option 1, purchase for a cash price of $675,000 with a useful life of 28 years. Option 2, lease for 28 years with annual lease payments of $72,000 at the beginning of the year. Option 3, purchase for 730,000 cash. The building is larger than needed and the company has the option of leasing the excess space for a net annual rental of $7,000 due at the end of each year. Which option would you recommend assuming an interest rate of 11.4%

**TV****M18 **– **Richard borrowed $92,000 on April 1st, 2020. This amount plus accrued interest at 10.6%, compounded semi-annually, is to be repaid April 1st, 2030. Richard plans to contribute to a debt retirement fund five equal amounts starting on April 1st, 2025, and for the next four years. The fund is expected to earn 9.5% per year. How much must Richard contribute each year to provide a fund to retire the debt on April 1st, 2030?**

**TVM20** -What amount should be deposited in a bank account today to grow to $15,000 three years from today? Use an interest rate of 8.5%.

TVM 21 – If $6,000 is deposited in a savings account today, what amount will be available four years from today? Use an interest rate of 8.5%.

TVM45 – ABC Corporation makes an investment today (January 1, 2019). They will receive $10,000 every December 31st for the next six years (2019 – 2025). If ABC wants to earn 11.5% on the investment, what is the most they should invest on January 1, 2019?

TVM 52 – On January 1, 2019, DEF Company decided to begin accumulating a fund for asset replacement five years later. The company plans to make five annual deposits of $60,000 at 8.5% each January 1 beginning in 2019. What will be the balance in the fund, on January 1, 2024 (one year after the last deposit)?

TVM54 – If $12,000 is deposited annually starting on January 1, 2019 and it earns 9.5%, what will the balance be on December 31, 2026?

TVM 56 – What amount should be recorded as the cost of a machine purchased December 31, 2019, which is to be financed by making 8 annual payments of $12,000 each beginning December 31, 2020? The applicable interest rate is 7.5%.

TVM61 – ABC Co. has a machine that cost $600,000. It is to be leased for 15 years with rent received at the beginning of each year. ABC wants a return of 9.5%. Compute the amount of the annual rent.

TVM 57 – How much must be deposited on January 1, 2019 in a savings account paying 5.5% annually in order to make annual withdrawals of $40,000 at the end of the years 2019 and 2020?

**TVM 67 – Richard has agreed to sell his business to his son. To make financing more convenient to his son, he agrees to sell the business for 7 annual payments of $6,000 each. The payments will begin 4 years from today. Assume an annual interest rate of 5.5%. What is the present value of the 7 payments? ****This situation is an ordinary annuity of 7 payments deferred 3 periods.**

**TVM68 – Richard plans to start a new business at the end of 7 years. Since he is strapped for cash, he plans to invest $8,000 only at the end of the fourth, fifth, sixth and seventh years. What is the future value of Richard’s investment at the end of the seventh year? Assume an interest rate of 7.5%.**