Question

What is the value today of $3,000 per year, at a discount rate of 8 percent, if the first payment is received 7 years from today and the last payment is received 25 years from today? (Do not round intermediate calculations and round your final answer to 2 decimal places, e.g., 32.16.) Please show formula and BAII solution if possible.

Answer 1

PV of Annuity = Cash Flow * [ 1 - (1+r)^-n ] / r

PV of Annuity starting from 7 Years = PV of ANnuity for 25 Years - PV of ANnuity for 6 Years

= [ 3000 * [ 1 - (1+0.08)^-25 ] / 0.08 ] - [ 3000 * [ 1 - (1+0.08)^-6 ] / 0.08 ]

= [ 3000 * [ 1 - (1.08)^-25 ] / 0.08 ] - [ 3000 * [ 1 - (1.08)^-6 ] / 0.08 ]

= [ 3000 * [ 1 - 0.1460 ] / 0.08 ] - [ 3000 * [ 1 - 0.6302 ] / 0.08 ]

= [ 3000 * [ 0.8540 ] / 0.08 ] - [ 3000 * [ 0.3698 ] / 0.08 ]

= $ 32025 - $ 13,867.5

= $ 18,157.5