CHAPTER 6
Accounting and the Time Value of Money
I. Interest – the time value of money 1. Interest is payment for the use of money. It is the excess cash received or repaid over and above the principal (amount lent or borrowed). Interest rates are generally stated on an annual basis unless indicated otherwise. Amount of interest depends on: a. b. c. d. the principal, the number of periods, the interest rate, and the way interest is computed. (1) Simple interest: interest is computed on the principal only. (2) Compounding interest: interest is computed on the principal and on any interest previously earned. You need to make sure that the time periods and the interest rate are consistent with each other, and both are consistent with the compounding factor.
II. Single Sum Problems 1. Single sum problems involve a single amount of money that either exists now or will in the future. Formula for future amount: FV = PV(FVFn, i) Where FV: Future value PV: present value FVFn, I: future value factor for n periods at i %, which can be found in Table 6-1. n: number of periods i: interest rate
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Formula for present value: PV = FV(PVFn, i) Where PVFn, I: present value factor for n periods at i %, which can be found in Table 6-2.
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Four factors in single sum type of problems: FV, PV, n, and i. If you know any three of the four factors, you can always find out the fourth one using either the present value formula or the future value formula. The process of finding the future amount is called accumulation. The process of finding the present value is called discounting. The factors in Table 6-2 are the reciprocal of corresponding factors in Table 6-1.
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6-1
III. Annuity Problems Annuity problems involve a series of equal periodic payments or receipts called rents. Three types of annuities: (1) In an ordinary annuity the rents occur at the end of each period. The first rent will occur one period from now. In an annuity due the rents occur at the beginning of each period. The first rent will occur now. In a deferred annuity the rents occur in the future. In an ordinary annuity of n rents deferred for y periods the first rent will occur (y + 1) periods from now. In an annuity due of n rents deferred for y periods the first rent will occur y periods from now.
In annuity problems, the rents, interest payments, and number of periods must all be stated on the same basis. For the purpose of looking up interest factors, n equals the number of "periods" and is always equal to the number of rents.
B. Annuity Due Problems 1. Formula for future value of annuity due: FVAD = R x (FVF – OAn, i ) x (1 + i) Where FVAD: Future value of annuity due R: periodic rent (FVF – OAn, i): future value of ordinary annuity interest factor for n periods at i %, which can be found in Table 6-3. please notice that no separate interest table is needed for the computation of future value of an annuity due.
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A. Ordinary Annuity Problems 1. Formula for future value of an ordinary annuity FVOA = R(FVF – OAn, i) Where FVOA: Future value of ordinary annuity R: periodic rent (FVF – OAn, i): future value of ordinary annuity of factor for n periods at i %, which can be found in Table 6-3. 2. Formula for present value of an ordinary annuity: PVOA = R(PVF – OAn, i) Where PVOA: Present value of ordinary annuity R: periodic rent (PVF – OAn, i): present value of ordinary annuity of factor for n periods at i %, which can be found in Table 6-4. The factors in Tables 6-3 and 6-4 are not reciprocals of each other. 6-2
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Formula for present value of annuity due: PVAD = R(PVF – ADn, i ) Where PVAD: present value of annuity due R: periodic rent (PVF – ADn, i): present value of annuity due interest factor for n periods at i %, which can be found in Table 6-3.
C. Deferred Annuity Problems A deferred annuity does not begin to produce rents until two or more periods have expired. A deferred annuity problem can be solved using the present/future value of ordinary annuities.