How much money is needed to establish a fund paying $80,000 annually forever with the first payment made immediately if the fund will earn interest at 5% p.a. compounded semi-annually?

To solve this problem, we need to understand the concept of perpetuity. A perpetuity is an infinite series of equal payments made at regular intervals. The present value of a perpetuity can be calculated using the formula:

PV = PMT / r

where:

• PV is the present value or the initial investment needed
• PMT is the payment per period
• r is the interest rate per period

In this case, the payment (PMT) is $80,000 per year and the interest rate (r) is 5% per year. However, since the interest is compounded semi-annually, we need to adjust these values accordingly.

The semi-annual payment is $80,000 / 2 =$40,000. The semi-annual interest rate is 5% / 2 = 2.5% or 0.025 in decimal form.

Now we can substitute these values into the formula:

PV = $40,000 / 0.025 =$1,600,000

Therefore, $1,600,000 is needed to establish a fund paying$80,000 annually forever with the first payment made immediately if the fund will earn interest at 5% per annum compounded semi-annually.