Math
posted by Terri on .
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?

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^n1)/(1.021)
= 150000*1.02^n + 3000(1.02^n1)/.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 
Oops. the formula is
150000(1.02^n + 1.02^(n+1)  1)
so $1,327,258.06 
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