If an annuity can make an unending number of equal payments at the end of the interest periods, it is called a perpetuity. If a lump sum investment of An is needed to result in n periodic payments of R when the interest rate per period is i, then

An R1-(1+i)-

(a) Evaluate lim n→[infinity] An to find a formula for the lump sum payment for a perpetuity.

(b) Find the lump sum investment needed to make payments of $90 per month in perpetuity if interest is 6%, compounded monthly. (Round your answer to the nearest cent.)
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