Final answer:
To determine the amount needed today to generate a 5-year annuity at 12% interest with $1,000 annual payments, the present value annuity formula is used, which calculates to $3,604.78.
Step-by-step explanation:
The question asks to find the present value of a 5-year annuity with annual payments of $1,000, starting one year from today, at a 12% interest rate. To calculate this, we use the present value formula for an annuity:
PV = PMT × ((1 - (1 + r)^{-n}) / r)
Where:
PV is the present value,PMT is the annual payment ($1,000),r is the interest rate per period (12% or 0.12), andn is the number of periods (5 years).
Substituting the values into the formula, we get:
PV = $1,000 × ((1 - (1 + 0.12)^{-5}) / 0.12)
After solving, the present value (PV) comes out to $3,604.78.
Therefore, the correct answer is c. $3,604.78.