# Math

Luis has \$150,000 in his retirement account at his present company. Because he is assuming a position with another company, Luis is planning to "roll over" his assets to a new account. Luis also plans to put \$3000/quarter into the new account until his retirement 20 years from now. If the new account earns interest at the rate of 8%/year compounded quarterly, how much will Luis have in his account at the time of his retirement?

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1. assuming he adds 3000 at the beginning of each quarter, the account will have

1 quarter: 150000*1.02+3000*1.02
2 qtrs: 150000*1.02^2 + 3000*(1.02^2 + 1.02)
n qtrs: 150000*1.02^n + 3000(1.02 + 1.02^2 + ... + 1.02^n)
= 150000*1.02^n + 3000 (1.02^n-1)/(1.02-1)
= 150000*1.02^n + 3000(1.02^n-1)/.02
= 150000(1.02^n + 1.02^n - 1)
= 150000(2*1.02^n - 1)

so, after 20 years (80 quarters), he will have \$1,312,631.75

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2. Oops. the formula is

150000(1.02^n + 1.02^(n+1) - 1)

so \$1,327,258.06

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3. 01832436288

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