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# Annuities: Investment for a group of physicians

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A representative of a reputable financial services company has approached you as a manager of a four-person group of anesthesiologists with an opportunity to purchase a 10-year annuity due for each member of the group. The annuity due would pay \$40,000 each year beginning 5 years from now (i.e. at time = 5). What is the most you would be willing to pay now, per each physician, for this investment? Assume an appropriate discount rate of 7%.

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#### Solution Preview

This would be an annuity due (the difference between annuity due and normal annuity is that in annuity due payments are at start of year whereas in normal annuity payments are at end of year).

The formula for the present value of an annuity due, sometimes also called an immediate annuity, is used to calculate a series of periodic payments that start immediately i.e. its paid at the beginning of periods.

(1+i) *P* [(1 - (1+ i) ^ (- n))/i]

P = periodic payment
i = interest rate per period
n = number of periods

This formula would give the value of the payments at the time of the first payment.
In this problem ...

#### Solution Summary

A step by step explanation of the calculation of an annuity due

\$2.19