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Tanja wants to establish an account that will supplement her retirement income beginning 25 years from now. Find the lump sum she must deposit today so that $600,000 will be available at time of retirement, if the interest rate is 10%, compounded quarterly.

 Dec 29, 2022
 #1
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There are 4 quarters in a year, and we have a period of 25 years, so there are 4 x 25 = 100 quarters. 

 

So, the account is \(1.1^{100} = 13780.6123398\) times the initial deposit. 

 

So, we have \(13780.6123398x = 600,000\), meaning \(x \approx \color{brown}\boxed{43.54}\)

 Dec 29, 2022
 #2
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PV = FV / [1  +  R / m]^(N*m)

 

PV ==600,000 / [1  +  0.10 / 4]^(25 *4)

 

PV ==600,000 / [1  +  0.025]^100

 

PV ==600,000 / 1.025^100

 

PV ==600,000 / 11.813716351

 

PV ==$50,788.42 - what Tanya must deposit today in order to have $600,000 25 years from now.

 Dec 29, 2022

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