Final answer:
The present value of the deferred annuity can be calculated using the formula for present value of an annuity. In this case, we are given a series of 12 semiannual payments of $2,700 starting 6 1/2 years from today. The discount rate is 7.7% compounded semiannually. Therefore, the present value of this deferred annuity is $18,714.12.
Step-by-step explanation:
The present value of the deferred annuity can be calculated using the formula for present value of an annuity. In this case, we are given a series of 12 semiannual payments of $2,700 starting 6 1/2 years from today. The discount rate is 7.7% compounded semiannually.
- First, we calculate the present value of each semiannual payment using the formula:
PV = Payment ÷ (1 + r/n)^(n*t), where PV is the present value, Payment is the payment amount, r is the discount rate, n is the number of compounding periods per year, and t is the number of years.
PV = $2,700 ÷ (1 + 0.077/2)^(2*6.5) = $1,559.51 - Next, we calculate the total present value of the annuity by summing up the present values of all the payments:
Total Present Value = PV * Number of Payments
Total Present Value = $1,559.51 * 12 = $18,714.12
Therefore, the present value of this deferred annuity is $18,714.12.