Question

An annuity provides for 30 annual payments. The first payment of 100 is made immediately and the remaining payments increase by 8 percent per annum. Interest is calculated at 13.4 percent per annum. Calculate the present value of this annuity.

Answer 1

The present value of this annuity is approximately $720.60.

Step-by-step explanation:

To calculate the present value of this annuity, we can use the formula for the present value of an increasing annuity:

PV = C[1 - (1+r)^-n]/(r - g)

Where PV is the present value, C is the initial payment, r is the interest rate, g is the growth rate, and n is the number of periods.

In this case, the initial payment is $100, the interest rate is 13.4%, the growth rate is 8%, and there are 30 annual payments.

Plugging these values into the formula, we get:

PV = $100[1 - (1+0.134)^-30]/(0.134 - 0.08)

Performing the calculations, the present value of this annuity is approximately $720.60.