Choice "B" is correct. The facts of the question provide annuity factors, yet the question only provides one "annuity" - the $30,000 for the first two years. Therefore, to calculate the present value of the savings for years 1 and 2, the factor for the present value of an annuity of $1 for two periods (1.65) is used. To calculate the present value of the savings for year 3, the factor for the lump sum of a present value of $1 for three periods is required; however, it is not directly provided. The factor must be calculated as the difference between the factors for the present value of an annuity of $1 for three periods (2.32) and for two periods (1.65), or .67. Years 1 & 2 | $30,000 × 1.65 | $49,500 | Year 3 | $20,000 × (2.32 − 1.65) | 13,400 | | | $62,900 |
Review your knowledge of how the annuity and lump sum factors work together, as follows: PV of Year 1: $30,000 × 0.88 | = | $26,400 | PV of Year 2: $30,000 × 0.77 [1.65 − 0.88] | = | 23,100 | PV of Year 3: $20,000 × 0.67 [2.32 − 1.65] | = | 13,400 | | Total PV of Future Savings | | $62,900 |
The present value of $1 is equal to the difference between the present value of an annuity for the appropriate sequential periods. |
