Question

starting 8 years from today, you will receive $1,000 per year payable continuously for 15 years. if the rate of interest compounded continuously is 3%, what is the present value of this continuous annuity?

Answer 1

The present value of the continuous annuity is approximately $9772.74.

Step-by-step explanation:

The present value of a continuous annuity can be calculated using the formula:

PV = P/(1+r)^t

where PV is the present value, P is the payment per period, r is the interest rate, and t is the number of periods. In this case, the payment is $1,000 per year, the interest rate is 3%, and the number of periods is 15 years. Plugging in these values into the formula, we get:

PV = 1000/(1+0.03)^15

PV ≈ $9772.74

Therefore, the present value of the continuous annuity is approximately $9772.74.

Answer 2

The present value of this continuous annuity is $33,333.33.

Step-by-step explanation:

An annuity is a financial product that provides a series of payments at equal intervals. Typically used for retirement planning, annuities offer a steady income stream, often purchased with a lump sum. Various types include fixed, variable, and indexed annuities, each with distinct features and benefits.

To calculate the present value of a continuous annuity, we can use the formula: PV = PMT / r,

where PV is the present value, PMT is the payment per year, and r is the interest rate. In this case, the payment per year is $1,000, and the interest rate is 3%.

Therefore, the present value of this continuous annuity is -

= $1,000 / 0.03

= $33,333.33.