TV Problems

PRACTICE PROBLEM SET – TIME VALUE OF MONEY

Answers are in [brackets]

1. An investor deposited $10,000 in a savings account paying 5% converted quarterly. At the end of 5 years what will be the value of the account. [$12,820.37]

2. A depositor planned to leave $2,000 in a savings account paying 5% converted semiannually for 5 years. However, at the end of 2 1/2 years the depositor had to withdraw $1,000. What amount will be in the account at the end of the original 5 year period? [1,428.76]

3. Find the value of $1,000 invested at 8% for 10 years with interest compounded annually. [$2,158.93]

4. Find the amount of $6,000 invested at 12% for 5 years, compounded -- Annually, [$10,574.05]

Semi-Annually, [$10,745.09]

Quarterly, [$10,836.67]

Monthly, [$10,900.18]

Daily, [$10,931.63]

5. Find the present value of $5,000 due in 4 years if money is worth 4% compounded semi-annually. [$4,267.45]

6. What is the present value of a certificate of deposit with a maturity value of $1,000 due in 3 years, if money is worth 6% compounded semi-annually? [$837.48]

7. A person can buy a piece of property for $4500 cash OR for $2000 down and $3000 in 3 years. If money is earning 6% compounded semi-annually, which is the better purchase plan and by how much? [pay in cash $4500., you would be better off by $12.45]

8. A piece of property can be purchased for $2850 cash OR for $3000 in 12 months. Which is the better plan if money is worth 7% compounded quarterly? [pay in payments, you would be better off by $52.12]

9. Find the amount of an annuity of $5,000 per year for 10 years at 6% and 7% with interest compounded annually.[6%=$65,903.98; 7%=$69,082.24]

10. What is the value of an annuity of $100 paid monthly for 6 years if money is worth 6% compounded monthly? [$8640.89]

11. An investor wants to provide for a $3000 scholarship every year for 10 years. If the school can get a 5.5% return on its investment, how much money should the investor give now? [$22,612.88]

12. Wilson agrees to pay Smith $1000 each year for 5 years. If money is worth 7% what is the cash equivalent of this debt? [$4100.20]

13. If money is worth 9% converted semi-annually, what is the present value of $145.50 due every 6 months for 2 years? [$521.99]

14. An investor wants to save for five years for a down payment on a house. She deposits $200 per month into a savings account paying 7% compounded monthly. At the end of the five years, she places the balance of the savings account as a down payment on a house costing $79,308.00. What will her monthly house payments be if she finances it for 25 years at 7%? [$459.33]

15. An investor makes a $2000 annual deposit into a mutual fund that produces a return of 12% annually for 3 years. How much will the investor have at the end of the three year term? [$6748.80]

16. What are the monthly payments of a $2600 loan at 17 1/2% for one year using a) simple interest and b) add-on method. c) How much money would be saved by making the simple interest loan? [ a) $237.75. b) $254.58 c) $202]

17. What is the effective interest rate of a discount loan for $2600 at 17 1/2% for one year? [21.21%]

18. What is the most economical loan to the borrower: a) a simple interest loan for 18% for one year or b) an add-on loan for 15 1/2% for one year . Each loan calculated on $5000 of principal. [simple interest by $275]

19. What is the annual yield on:

a) a 3% account compounded monthly, [3.04%]

b) a 6 1/8% account compounded daily, [6.32%]

c) a 4 1/2% account compounded annually, [4.50%]

d) a 9% account compounded semi-annually, [9.20%]

20. An investor saves $500 per quarter in an IRA account for 30 years at 7 3/4% interest compounded quarterly. At the end of 30 years, she wants to pay herself equal (annual) payments for the next 25 years. If money continues to be worth 7.75%, how much will the annual payments be? [$21,299.13]

21. A city’s population is expected to increase at a rate of 4.95% per year for the next ten years. If the current population is 322,000, what is the expected population at the end of the next ten years? [522,012]

22. Find the amount of $6000 for 8 years at 8% compounded a) annually, b) semiannually, c) quarterly, d) monthly. [a=$11,105.58, b=$11,237.89, c=$11,307.24, d=$11,357.74]

23. $2000 is deposited into an account earning 6.75%. What is the balance of this account in 6 years, 8 months if interest is compounded monthly? [$3,132.67]

24. An investment of $4000 is made for 12 years. During the first 5 years the interest rate is 7% compounded semiannually; the rate then drops to 6% for the remainder of the time. What is the final amount? [$8,534.64]

25. The University is given a gift of $400,000 for construction of a science building. The University receives 8% on the money for 9 years then the rate drops to 7%. If the building is constructed 25 years after the gift was received, how much is in the fund at that time? [$2,360,555.60]

26. What principal is needed to accumulate $3000 in 8 years at 4.5% interest compounded semiannually? [$2,101.40]

27. What is the present value at 4% compounded quarterly of $12,000 due in 18 months? [$11,304.54]

28. A person owns a note for $2500 due in 5 years. What should a buyer pay for the note if money is worth 5% compounded quarterly? [$1,950.02]

29. Find the present value of $2000 due in 15 months if money is worth 7% compounded semiannually? [$1,835.46}

30. A University alumni wanted to set aside an amount such that $250,000 will accumulate in 50 years to give to the University. What should she set aside now to provide for the gift if money is worth 6% compounded monthly? [$12,540.16]

31. An investor deposits $1000 per year into an account earning 8.125% compounded annually for 14 years. At that time, she stops contributing, the balance in the account continues to grow for another 11 years (at the same interest rate). What is the balance at the end of the term? [$57,679.45]

32. An investor’s IRA grows with $2,000 annual deposits and earns 9% for 30 years. The sum is used to live off of for the next 30 years. What is the value of the annuity before the withdrawals and what is the amount of the annual withdrawals? [$272,615.08, $26,535.36]

33. $500 rent payments are paid to a landlord. What is the value of 5 years of monthly payments if money is worth 6.5% compounded monthly? [$35,336.98]

34. $200 monthly deposits are made into a mutual fund that earns 12.25% compounded monthly. What is the value of the account at the end of 7.25 years? [$27,813.53]

35. What is the monthly payment of a $28,000 car loan at 9.62% interest for 5 years? [$589.70] How much is paid to the principal? [$28,000] How much is paid to interest? [$7,382]

36. The landlord holding a $400 per month, four year lease wants to sell the obligation to a bank. With money worth 7.15%, (compounded monthly), how much will the bank pay for the lease? [$16,655.63] What does the bank earn from this transaction? [$2,544.37]

37. To retire with $1,000,000 in 40 years, how much would have to be deposited monthly to meet the goal if money is worth 7.375%? [$342.69] How much principal is paid into the account? [$164,491.20] How much interest was earned? [$835,508.80]

38. What is the current cash value of $2500 annual payments for 8 years with money worth 6.175% compounded annually? [$15,417.53]

39. In 5 years, your annual salary will be $47,500 if you receive 8.2% annual raises. What is your current salary? [$32,030]