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at an interest rate of 10% per year, the length of time required from time zero to recover an initial investment of $10,000 by receipts of $1,000 per year beginning in year three is nearest to: a) 10 years b) 20 years c) 100 years d) never

Respuesta :

Initial investment can never be recovered.

Let the present value of a regular perpetuity be = pv

Annual cash flow = cf = $1,000

Interest rate = r = 10

If the initial payment begins in one year, then the present value of the regular perpetuity will be  -

PV = CF/r

PV = 1,000/0.1

PV = 10,000

Therefore,

The flow of infinite payments beginning next year is equivalent to $10,000.

However, if the payment begin in third year, the first two payments will be missing and the present value of deferred payments can never be equal to $10,000.

Thus, initial investment can never be recovered.

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