If an annuity makes an infinite series 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, thenAn = R[(1-(1+i)^-n)/(i)](a) Evaluatelim n→∞ Anto find a formula for the lump sum payment for a perpetuity.  (b) Find the lump sum investment needed to make payments of $180 per month in perpetuity if interest is 6%, compounded monthly. (Round your answer to the nearest cent.)$

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Asked Oct 17, 2019
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If an annuity makes an infinite series 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 = R[(1-(1+i)^-n)/(i)]

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


(b) Find the lump sum investment needed to make payments of $180 per month in perpetuity if interest is 6%, compounded monthly. (Round your answer to the nearest cent.)
$
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Expert Answer

Step 1

Given:

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(1-(1+) -2 i

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Step 2

(a). Find the limit

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[1-(1+)") lim AR i (1-(1+i)") lim A, lim R i 1-(1-)") = R 1 1- (1+) - R "संव (1-0) - R 1 - R

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Step 3

(b). Finding the lump investment needed to make payments of $180 pe...

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