Question

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 A_n 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→∞ A_n  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.)
$

Answer 1

PART(a):

The lump sum investment of An is given by

1- (1+) An R

the lump sum payment for perpetuity is given by

1 (1i) -n Aolim R i noo

plugin the limit,

1 - (1i ) As R

1 - 0 As=R i

Ao

PART(b):

1- (1+) An R

plugin the values

A1290 (1 +0.06) 0.06 121

A12 754.545954634

rounding off to nearest cent,

A12 754.55

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