A personal account earmarked as a retirement supplement contains $342,100. Suppose $300,000 is used to establish an annuity that earns 5%, compounded quarterly, and pays $6500 at the end of each quarter. How long will it be until the account balance is $0?

Question

Semaj Morris

Business

5 July, 17:17

A personal account earmarked as a retirement supplement contains $342,100. Suppose $300,000 is used to establish an annuity that earns 5%, compounded quarterly, and pays $6500 at the end of each quarter. How long will it be until the account balance is $0?

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Juliette Sharp · Answer 1

Therefore, 144 quarters are required until the account balance is $0

Explanation:

Present Value=Quarterly payment * (1 - ((1+r) ^ (-n)) / n

$3,00,000 = $4500 * (1 - ((1+0.0125) ^ (-n)) / 0.0125

$3,00,000 = $360000 * (1 - ((1+0.0125) ^ (-n))

(1 - ((1.0125) ^ (-n)) = $300000 / $360000

(1 - ((1.0125) ^ (-n)) = 0.833333

n = 144