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CalculusQ&A LibraryIf 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 $180 per month in perpetuity if interest is 6%, compounded monthly. (Round your answer to the nearest cent.)$Question

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 *A _{n}* is needed to result in

A_{n} = R[(1-(1+i)^-n)/(i)]

(a) Evaluate

(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.)

$

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 $180 per month in perpetuity if interest is 6%, compounded monthly. (Round your answer to the nearest cent.)

$

Step 1

Given:

Step 2

(a). Find the limit

Step 3

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

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