_________________________________________________________________________
1. Future Value of a Single Sum
a. Future Value = Present Value x FVFn,i
b. FVFn,i = Future Value
Present Value
(1) “I” unknown and “n” known, or Trace solved factor to Table 1. (2) “n” unknown and “I ” known Trace solved factor to Table 1.
TIP: The present value amount is sometimes called the principal.
2. Present Value of a Single Sum
a. Present Value = Future Value x PVFn,i
b. PVFn,i = Present Value
Future Value
(1) “i ” unknown and “n” known, or Trace solved factor to Table 2. (2) “n” unknown and “i ” known Trace solved factor to Table 2.
3. Future Value of an Ordinary Annuity
a. Future Value of an Ordinary Annuity = Rent x FVF-OAn,i
b. Rent = Future Value of an Ordinary Annuity
FVF-OAn,i
c. FVF-OAn,i = Future Value of an Ordinary Annuity Rent
(1) “i” unknown and “n” known, or Trace solved factor to Table 3. (2) “n” unknown and “i” known Trace solved factor to Table 3.
4. Present Value of an Ordinary Annuity
a. Present Value of an Ordinary Annuity = Rent x PVF-OAn,i
b. Rent = Present Value of an Ordinary Annuity
PVF-OAn,i
c. PVF-OAn,i = Present Value of an Ordinary Annuity Rent
(1) “i ” unknown and “n” known, or Trace solved factor to Table 4. (2) “n” unknown and “i ” known Trace solved factor to Table 4.
Accounting and the Time Value of Money 6-15 ____________________________________________________________________________
ILLUSTRATION 6-5
(Continued)___________________________________________________________________________
5. Future Value of an Annuity Due
a. Future Value of an Annuity Due = Rent x FVF-ADn,i
b. Rent = Future Value of an Annuity Due
FVF-ADn,i
TIP: There is no table in this book for Future Value of an Annuity Due, so ordinary annuity factors must be modified as follows:
FVF-ADn,i = FVF-OAn,i X (1 + i) OR FVF-ADn,i = FVF-OAn+1,i - 1.00000
6. Present Value of an Annuity Due
a. Present Value of an Annuity Due = Rent x PVF-ADn,i
b. Rent = Present Value of an Annuity Due
PVF-ADn,i
c. PVF-ADn,i = Present Value of an Annuity Due
Rent
(1) “i ” unknown and “n” known, or Trace solved factor to Table 5. (2) “n” unknown and “i ” known Trace solved factor to Table 5.
TIP: Factors for the present value of an annuity due can be derived by adjusting factors from the Table for Present Value of an Ordinary Annuity as follows:
PVF-ADn,i = PVF-OAn,i X (1 + i) OR PVF-ADn,i = PVF-OAn-1,i + 1.00000 ---
Abbreviations:
i = Interest Rate
n = Number of Periods or Rents
FVFn,i = Future Value of 1 Factor for n periods at i interest PVFn,i = Present Value of 1 Factor for n periods at i interest
FVF-OAn,i = Future Amount of an Ordinary Annuity of 1 Factor for n periods at i interest PVF-OAn,i = Present Value of an Ordinary Annuity of 1 Factor for n periods at i interest FVF-ADn,i = Future Amount of an Annuity Due of 1 Factor for n periods at i interest PVF-ADn,i = Present Value of an Annuity Due of 1 Factor for n periods at i interest ___________________________________________________________________________
6-16 Problem Solving Survival Guide for Intermediate Accounting, 15th Edition
____________________________________________________________________________
EXERCISE 6-1
Purpose:
(L.O. 3) This exercise will test your knowledge of the applicability of the fivecompound interest tables discussed in this chapter.
Instructions
For each independent situation below, (1) indicate which table you would need to use in order to locate the appropriate factor to solve for the figure requested, and (2) indicate if you divide (D) or multiply (M) by that factor to solve for the figure requested. Use the appropriate numerals and letters to indicate your answer for each.
I. Future Value of 1 II. Present Value of 1
III. Future Value of an Ordinary Annuity of 1 IV. Present Value of an Ordinary Annuity of 1 V. Present Value of an Annuity Due of 1
TIP: There are two approaches to solving problems involving present value or future value of a single
sum; there is only one approach available for solving annuity problems.
(1) (2)
_____ _____ 1. $1,000 is put on deposit today to earn 6% interest, compounded annually. How much will be on deposit at the end of 8 years?
_____ _____ 2. What amount today is equivalent to receiving $600 at the end of every year for 6 years, assuming interest is compounded annually at the rate of 5%?
_____ _____ 3. If you wish to be able to withdraw the sum of $8,000 at the end of 12 years, how much do you have to deposit today, assuming interest is compounded annually at the rate of 6%?
_____ _____ 4. If $400 is put in a savings account at the end of every year for 5 years, how much will be accumulated in the account if all amounts that remain on deposit earn 6% interest, compounded annually?
_____ _____ 5. What amount today is equivalent to receiving $1,000 ten years from now if interest of 7% is compounded annually?
_____ _____ 6. What amount today is equivalent to receiving $1,000 at the end of each year for ten years if interest of 7% is compounded annually?
_____ _____ 7. How much must be deposited today to allow for the withdrawal of $1,000 at the end of each year for ten years if interest of 7% is compounded annually?
_____ _____ 8. What is the present value of $500 due in 8 years at 6% compounded interest?
_____ _____ 9. What is the future value of an ordinary annuity of $100 per period for 6 years at 7% compounded interest?
Accounting and the Time Value of Money 6-17 ____________________________________________________________________________
_____ _____ 10. How much money must be deposited today to be able to withdraw $700 at the end of 7 years, assuming 7% compounded interest?
_____ _____ 11. How much money must be deposited today to be able to withdraw $700 at the beginning of each of 7 years, assuming 7% compounded interest? _____ _____ 12. What is the discounted value of $700 due in 7 years at a 7% compounded
interest rate?
_____ _____ 13. What is the future value of $700 put on deposit now for 7 years at 7% compounded interest?
_____ _____ 14. What is the future value in seven years of $700 put on deposit at the end of each of 7 years if all amounts on deposit earn 7% compound interest? _____ _____ 15. How much can be withdrawn at the end of 5 years if $1,000 is deposited
now at a 6% compound interest rate?
_____ _____ 16. What amount can be withdrawn at the end of each period for five years if $1,000 is deposited now and all amounts on deposit earn 6% interest compounded annually?
_____ _____ 17. If a debt of $5,000 is to be repaid in five equal beginning-of-year installments, what is the amount of each installment if interest at 7% is charged on the unpaid balance?
_____ _____ 18. What amount must be deposited at the end of each of four years to accumulate a fund of $7,000 at the end of the fourth year, assuming interest at a rate of 6% compounded annually?
6-18 Problem Solving Survival Guide for Intermediate Accounting, 15th Edition ____________________________________________________________________________
Solution to Exercise 6-1
1. I M or II D 2. IV M 3. II M or I D 4. III M 5. II M or I D 6. IV M 7. IV M 8. II M or I D 9. III M 10. II M or I D 11. V M 12. II M or I D 13. I M or II D 14. III M 15. I M or II D 16. IV D 17. V D 18. III DApproach and Explanation: Draw a time diagram and place each fact given in the appropriate
position on the diagram. Determine what is to be solved for in the question. Think about the content of each of the five compound interest tables included at the end of this chapter. Review the use of the interest factors as summarized in Illustration 6-5. The titles and the contents of the five interest tables are as follows:
1. Future Value of 1 Table. Contains the amount to which $1 will accumulate if
deposited now at a specified rate of interest and left for a specified number of periods (Table 1).
2. Present Value of 1 Table. Contains the amount that must be deposited now at a
specified rate of interest to equal $1 at the end of a specified number of periods (Table 2).
3. Future Value of an Ordinary Annuity of 1 Table. Contains the amount to which
periodic rents of $1 will accumulate if the payments (rents) are invested at the
end of each period at a specified rate of interest for a specified number of periods (Table 3).
4. Present Value of an Ordinary Annuity of 1 Table. Contains the amount that
must be deposited now at a specified rate of interest to permit withdrawals of $1 at the end of regular periodic intervals for the specified number of periods (Table 4).
5. Present Value of an Annuity Due of 1 Table. Contains the amount that must be
deposited now at a specified rate of interest to permit withdrawals of $1 at the