Your grandparents would like to establish a trust fund that will pay you and your heirs $120,000 per year forever with the first payment 9 years from today. If the trust fund earns an annual return of 2.3 percent, how much must your grandparents deposit today

$4,349,590.19

Explanation:

An perpetuity is a series of equal cash flows payable for life or foreseeable future

Where the first payment is expected at a date later than year 1 , it is called and advanced perpetuity.

To determine the worth today (present value) for an advanced perpetuity, follow the steps below

Step 1:

Determine the  present value (PV ) of the perpetuity as though it is a standard perpetuity

PV of standard perpetuity =  A/r

r- 2.3%, A - 120,000

PV = 120,000/ 0.023

    = $5,217,391.30 (PV in year 8)

Note The PV formula helps to determine the PV at a year before the first one occurs, so because the first payment is expected in year 9, the PV is ascertained to be in year 8 terms.

Step 2:

Re-discount The PV in step 1 to year 0:

PV in year 0 = Cash flow × (1+r)^(-n)

               = 5,217,391.30 × (1.023)^(-8)

               = $4,349,590.19

My grandparents should deposit = $4,349,590.19

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