Question

An annuity-immediate has annual payments of amount P for 10 years. At a nominal rate of interest of 10% compounded quarterly, the present value of the annuity is $10,000. What is the amount of the annual payment P?

Answer 1

To find the annual payment of an annuity-immediate, use the present value formula.

Step-by-step explanation:

To find the annual payment of an annuity-immediate, we need to use the present value formula. The present value formula for an annuity-immediate is:

PV = P * (1 - (1 + r/n)^(-nt))/(r/n)

Where PV is the present value, P is the annual payment, r is the nominal interest rate, n is the number of compounding periods per year, and t is the number of years.

In this case, the present value of the annuity is $10,000, the nominal interest rate is 10% compounded quarterly, and the duration is 10 years. Plugging these values into the formula, we have:

$10,000 = P * (1 - (1 + 0.10/4)^(-4*10))/(0.10/4)

Simplifying the formula, we get:

$10,000 = P * (1 - (1 + 0.025)^(-40))/(0.025)

To find the value of P, we can rearrange the formula:

P = $10,000 * (0.025) / (1 - (1 + 0.025)^(-40))

Solving this equation, we find that the annual payment P is approximately $1,556.81.