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emmasim [6.3K]
3 years ago
14

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
Business
1 answer:
natali 33 [55]3 years ago
7 0

Answer:

$4,349,590.19

Explanation:

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

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

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

<em>Step 1:</em>

<em>Determine the  present value (PV ) of the perpetuity as though it is a standard perpetuity</em>

<em>PV of standard perpetuity =  A/r</em>

<em>r</em>- 2.3%, A - 120,000

PV = 120,000/ 0.023

    = $5,217,391.30 (PV in year 8)

<em>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.</em>

Step 2:

<em>Re-discount The PV in step 1 to year 0:</em>

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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